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5 (five) is a
number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual number ...
, numeral and digit. It is the
natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called '' cardinal ...
, and
cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. ...
, following 4 and preceding 6, and is a
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
. It has attained significance throughout history in part because typical humans have five digits on each hand.


In mathematics

5 is the third smallest
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
, and the second
super-prime Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins :3, 5, 11, 17, 31 ...
. It is the first safe prime, the first good prime, the first
balanced prime In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, given a prime number p_n, where is it ...
, and the first of three known
Wilson prime In number theory, a Wilson prime is a prime number p such that p^2 divides (p-1)!+1, where "!" denotes the factorial function; compare this with Wilson's theorem, which states that every prime p divides (p-1)!+1. Both are named for 18th-centu ...
s. Five is the second Fermat prime and the third
Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17 ...
exponent, as well as the third Catalan number, and the third Sophie Germain prime. Notably, 5 is equal to the sum of the ''only'' consecutive primes, 2 + 3, and is the only number that is part of more than one pair of twin primes, ( 3, 5) and (5, 7). It is also a
sexy prime In number theory, sexy primes are prime numbers that differ from each other by 6. For example, the numbers 5 and 11 are both sexy primes, because both are prime and . The term "sexy prime" is a pun stemming from the Latin word for six: . If ...
with the fifth prime number and first prime repunit, 11. Five is the third factorial prime, an alternating factorial, and an Eisenstein prime with no imaginary part and real part of the form 3p1. In particular, five is the first congruent number, since it is the length of the hypotenuse of the smallest integer-sided right triangle. Five is the second Fermat prime of the form 2^+ 1, and more generally the second Sierpiński number of the first kind, n^n+ 1. There are a total of five known Fermat primes, which also include 3, 17, 257, and 65537. The sum of the first 3 Fermat primes, 3, 5 and 17, yields 25 or 52, while 257 is the 55th prime number. Combinations from these 5 Fermat primes generate 31 polygons with an
odd Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric. Odd may also refer to: Acronym * ODD (Text Encoding Initiative) ("One Document Does it all"), an abstracted literate-programming format for describing X ...
number of sides that can be construncted purely with a compass and straight-edge, which includes the five-sided regular pentagon. Apropos, 31 is also equal to the sum of the maximum number of
area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an op ...
s inside a circle that are formed from the sides and diagonals of the first five n-sided polygons, and equal to the maximum number of areas formed by a six-sided polygon; per Moser's circle problem. The number 5 is the fifth Fibonacci number, being 2 plus 3. It is the only Fibonacci number that is equal to its position aside from 1, which is both the first and second Fibonacci numbers. Five is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), ... ( lists Markov numbers that appear in solutions where one of the other two terms is 5). Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers. 5 is the third Mersenne prime exponent of the form 2^n1, which yields 31: the prime index of the third
Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17 ...
and second double Mersenne prime 127, as well as the third double Mersenne prime exponent for the number
2,147,483,647 The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes. The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Dani ...
, which is the largest value that a signed 32-bit integer field can hold. There are only four known double Mersenne prime numbers, with a fifth candidate double Mersenne prime M_ = 223058...93951 − 1 too large to compute with current computers. In a related sequence, the first 5 terms in the sequence of Catalan–Mersenne numbers M_ are the only known prime terms, with a sixth possible candidate in the order of 101037.7094. These prime sequences are conjectured to be prime up to a certain limit. Every odd number greater than 1 is the sum of at most five prime numbers, and every odd number greater than 5 is conjectured to be expressible as the sum of three prime numbers. Helfgtott has provided a proof of the latter, also known as the odd Goldbach conjecture, that is already widely acknowledged by mathematicians as it still undergoes
peer-review Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work ( peers). It functions as a form of self-regulation by qualified members of a profession within the relevant field. Peer revie ...
. The sums of the first five non-primes greater than zero 1 + 4 + 6 + 8 + 9 and the first five prime numbers 2 + 3 + 5 + 7 + 11 both equal 28; the 7th triangular number and like 6 a
perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. ...
, which also includes 496, the 31st triangular number and perfect number of the form 2^−1(2^1) with a p of 5, by the Euclid–Euler theorem. There are a total of five known unitary perfect numbers, which are numbers that are the sums of their positive proper unitary divisors. A sixth unitary number, if discovered, would have at least nine odd prime factors. Five is conjectured to be the only odd untouchable number, and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree. In figurate numbers, 5 is a pentagonal number, with the
sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called ...
of pentagonal numbers starting: 1, 5, 12, 22, 35, ... * 5 is a centered tetrahedral number: 1, 5, 15, 35, 69, ... Every centered tetrahedral number with an index of 2, 3 or 4
modulo In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is ...
5 is divisible by 5. * 5 is a square pyramidal number: 1, 5, 14, 30, 55, ... The sum of the first four members is 50 while the fifth indexed member in the sequence is 55. * 5 is a centered square number: 1, 5, 13, 25, 41, ... The fifth
square number In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The u ...
or 52 is 25, which features in the proportions of the two smallest (3, 4, 5) and (5, 12, 13) ''primitive'' Pythagorean triples. The factorial of five, or 5 ! = 120, is the sum of the first fifteen non-zero positive integers, and 15th triangular number, which in turn is the sum of the first five non-zero positive integers and 5th triangular number. 35, which is the fourth or fifth pentagonal and tetrahedral number, is equal to the sum of the first five triangular numbers: 1, 3, 6, 10, 15. 5 is the value of the central cell of the only non-trivial normal magic square, also called the ''Lo Shu'' square. Its 3 x 3 array of squares has a magic constant M of 15, where the sums of its rows, columns, and diagonals are all equal to fifteen. 5 is also the value of the central cell the only non-trivial order-3 normal magic hexagon that is made of nineteen cells. Polynomial equations of degree and below can be solved with radicals, while quintic equations of degree 5, and higher, cannot generally be so solved. This is the Abel–Ruffini theorem. This is related to the fact that the symmetric group \mathrm_ is a solvable group for ''n'' ⩽ 4 and not solvable for ''n'' ⩾ 5.
Euler's identity In mathematics, Euler's identity (also known as Euler's equation) is the equality e^ + 1 = 0 where : is Euler's number, the base of natural logarithms, : is the imaginary unit, which by definition satisfies , and : is pi, the ratio of the circ ...
, e^+ 1 = 0, contains five essential
number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual number ...
s used widely in mathematics: Archimedes' constant \pi, Euler's number e, the imaginary number i,
unity Unity may refer to: Buildings * Unity Building, Oregon, Illinois, US; a historic building * Unity Building (Chicago), Illinois, US; a skyscraper * Unity Buildings, Liverpool, UK; two buildings in England * Unity Chapel, Wyoming, Wisconsin, US; a ...
1, and zero 0, which makes this formula a renown example of beauty in mathematics.


In geometry

A pentagram, or five-pointed polygram, is the first proper
star polygon In geometry, a star polygon is a type of non- convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, certain notable ones can arise through truncation operatio ...
constructed from the diagonals of a regular pentagon as self-intersecting edges that are proportioned in golden ratio, \varphi. Its internal geometry appears prominently in Penrose tilings, and is a facet inside Kepler-Poinsot star polyhedra and Schläfli–Hess star polychora, represented by its Schläfli symbol . A similar figure to the pentagram is a five-pointed
simple Simple or SIMPLE may refer to: *Simplicity, the state or quality of being simple Arts and entertainment * ''Simple'' (album), by Andy Yorke, 2008, and its title track * "Simple" (Florida Georgia Line song), 2018 * "Simple", a song by Johnn ...
isotoxal In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal () or edge-transitive if its symmetries act transitively on its edges. Informally, this means that there is only one type of edge to the object: given ...
star ☆ without self-intersecting edges. Generally, star polytopes that are regular only exist in
dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
s 2 ⩽ n < 5. In
graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
, all graphs with 4 or fewer vertices are planar, however, there is a graph with 5 vertices that is not: ''K''5, the complete graph with 5 vertices, where every pair of distinct vertices in a pentagon is joined by unique edges belonging to a pentagram. By
Kuratowski's theorem In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states that a finite graph is planar if and only if it does not contain a subgraph that is a subd ...
, a finite graph is planar iff it does not contain a subgraph that is a subdivision of ''K''5, or the complete bipartite utility graph ''K''3,3. A similar graph is the Petersen graph, which is strongly connected and also nonplanar. It is most easily described as graph of a pentagram ''embedded'' inside a pentagon, with a total of 5 crossings, a
girth Girth may refer to: ;Mathematics * Girth (functional analysis), the length of the shortest centrally symmetric simple closed curve on the unit sphere of a Banach space * Girth (geometry), the perimeter of a parallel projection of a shape * Girth ...
of 5, and a Thue number of 5. The Petersen graph, which is also a distance-regular graph, is one of only 5 known connected vertex-transitive graphs with no Hamiltonian cycles.Royle, G
"Cubic Symmetric Graphs (The Foster Census)."
The automorphism group of the Petersen graph is the symmetric group \mathrm_ of
order Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of ...
120 = 5!. The chromatic number of the plane is at least five, depending on the choice of set-theoretical axioms: the minimum number of colors required to color the plane such that no pair of points at a distance of 1 has the same color. Whereas the hexagonal Golomb graph and the regular hexagonal tiling generate chromatic numbers of 4 and 7, respectively, a chromatic coloring of 5 can be attained under a more complicated graph where multiple four-coloring Moser spindles are linked so that no monochromatic triples exist in any coloring of the overall graph, as that would generate an equilateral arrangement that tends toward a purely hexagonal
structure A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such a ...
. The plane contains a total of five
Bravais lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n ...
s, or arrays of
points Point or points may refer to: Places * Point, Lewis, a peninsula in the Outer Hebrides, Scotland * Point, Texas, a city in Rains County, Texas, United States * Point, the NE tip and a ferry terminal of Lismore, Inner Hebrides, Scotland * Points ...
defined by discrete
translation Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between ''transla ...
operations:
hexagonal In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A '' regular hexagon'' has ...
, oblique, rectangular, centered rectangular, and square lattices. The plane can also be tiled monohedrally with convex
pentagons In geometry, a pentagon (from the Greek language, Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple polygon, simple pentagon is ...
in fifteen different ways, three of which have Laves tilings as special cases. Five points are needed to determine a
conic section In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a ...
, in the same way that two points are needed to determine a line. A Veronese surface in the projective plane \mathbb^5 of a conic generalizes a linear condition for a point to be contained inside a conic. There are 5 Platonic solids in
three-dimensional space Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informa ...
: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The dodecahedron in particular contains pentagonal faces, while the icosahedron, its
dual polyhedron In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the oth ...
, has a vertex figure that is a regular pentagon. There are also 5: ☆ Regular polyhedron compounds: the stella octangula, compound of five tetrahedra, compound of five cubes, compound of five octahedra, and compound of ten tetrahedra. Icosahedral symmetry \mathrm I_ is isomorphic to the alternating group on 5 letters \mathrm A_ of order 120, realized by actions on these uniform polyhedron compounds. ☆ Space-filling convex polyhedra: the triangular prism, hexagonal prism, cube, truncated octahedron, and gyrobifastigium. While the cube is the only Platonic solid that can tessellate space on its own, the truncated octahedron and the gyrobifastigium are the only Archimedean and Johnson solids, respectively, that can also tessellate space with their own copies. ☆ Cell-transitive parallelohedra: any parallelepiped, as well as the rhombic dodecahedron and elongated dodecahedron, and the hexagonal prism and truncated octahedron. The cube is a special case of a parallelepiped, with the rhombic dodecahedron the only
Catalan solid In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. There are 13 Catalan solids. They are named for the Belgian mathematician Eugène Catalan, who first described them in 1865. The Catalan so ...
to tessellate space on its own. ☆ Regular abstract polyhedra, which include the excavated dodecahedron and the dodecadodecahedron. They have combinatorial symmetries transitive on flags of their elements, with topologies equivalent to that of toroids and the ability to tile the
hyperbolic plane In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ' ...
. The
5-cell In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol . It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It ...
, or pentatope, is the self-dual fourth-dimensional analogue of the
tetrahedron In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all ...
, with Coxeter group symmetry \mathrm_ of order 120 = 5 ! and \mathrm_ group structure. Made of five tetrahedra, its Petrie polygon is a regular pentagon and its orthographic projection is equivalent to the complete graph ''K''5. It is one of six regular 4-polytopes, made of thirty-one elements: five vertices, ten edges, ten faces, five tetrahedral cells and one
4-face In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a ''polyhedron''. In more technical treatments of the geometry of polyhedra ...
. *A regular 120-cell, the dual ''polychoron'' to the regular 600-cell, can fit one hundred and twenty 5-cells. Also, five 24-cells fit inside a small stellated 120-cell, the first
stellation In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in ''n'' dimensions to form a new figure. Starting with an original figure, the process extends specif ...
of the 120-cell. *A subset of the vertices of the small stellated 120-cell are matched by the great duoantiprism star, which is the only uniform nonconvex ''duoantiprismatic'' solution in the fourth dimension, constructed from the polytope cartesian product and made of fifty
tetrahedra In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all th ...
, ten pentagrammic crossed antiprisms, ten pentagonal antiprisms, and fifty vertices. *The grand antiprism, which is the only known non-Wythoffian construction of a uniform polychoron, is made of twenty pentagonal antiprisms and three hundred tetrahedra, with a total of one hundred vertices and five hundred edges. *The abstract four-dimensional 57-cell is made of fifty-seven hemi-icosahedral cells, in-which five surround each edge. The 11-cell, another abstract 4-polytope with eleven vertices and fifty-five edges, is made of eleven hemi-dodecahedral cells each with fifteen dodecahedra. The skeleton of the hemi-dodecahedron is the Petersen graph. Overall, the fourth dimension contains five Weyl groups that form a finite number of uniform polychora: \mathrm A_, \mathrm B_, \mathrm D_, \mathrm F_, and \mathrm H_, with four of these Coxeter groups capable of generating the same finite forms without \mathrm D_; accompanied by a fifth or sixth general group of unique 4-prisms of Platonic and Archimedean solids. There are also a total of five Coxeter groups that generate non-prismatic Eucledian honeycombs in 4-space, alongside five compact hyperbolic Coxeter groups that generate five regular compact hyperbolic honeycombs with finite facets, as with the order-5 5-cell honeycomb and the order-5 120-cell honeycomb, both of which have five cells around each face. Compact hyperbolic honeycombs only exist through the fourth dimension, or rank 5, with paracompact hyperbolic solutions existing through rank 10. Likewise, analogues of three-dimensional icosahedral symmetry \mathrm_ or four-dimensional \mathrm_ symmetry do not exist in dimensions ''n'' ⩾ 5; however, there is the uniform prismatic group \mathrm_ × \mathrm_ in the fifth dimension which contains
prisms Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentar ...
of regular and uniform 4-polytopes that have \mathrm_ symmetry. The 5-simplex is the five-dimensional analogue of the 5-cell, or 4-simplex; the fifth iteration of n- simplexes in any n dimensions. The 5-simplex has the Coxeter group \mathrm_ as its symmetry group, of order 720 = 6 !, whose group structure is represented by the symmetric group \mathrm_, the only finite symmetric group which has an outer automorphism. The 5-cube, made of ten tesseracts and the 5-cell as its vertex figure, is also regular and one of thirty-one
uniform 5-polytope In geometry, a uniform 5-polytope is a five-dimensional uniform polytope. By definition, a uniform 5-polytope is vertex-transitive and constructed from uniform 4-polytope Facet (geometry), facets. The complete set of convex uniform 5-polytopes ...
s under the Coxeter \mathrm B_ hypercubic group. The
demipenteract In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a ''5-hypercube'' ( penteract) with alternated vertices removed. It was discovered by Thorold Gosset. Since it was the only semiregular ...
, with one hundred and twenty
cells Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Locations * Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...
, is the only fifth-dimensional semiregular polytope, and has the rectified 5-cell as its vertex figure, which is one of only three semiregular 4-polytopes alongside the rectified 600-cell and the
snub 24-cell In geometry, the snub 24-cell or snub disicositetrachoron is a convex uniform 4-polytope composed of 120 regular tetrahedral and 24 icosahedral cells. Five tetrahedra and three icosahedra meet at each vertex. In total it has 480 triangular face ...
. In the fifth dimension, there are five regular paracompact honeycombs, all with infinite facets and vertex figures. There are exclusively twelve complex aperiotopes in \mathbb^n complex spaces of dimensions n5, with fifteen in \mathbb^4 and sixteen in \mathbb^3; alongside complex polytopes in \mathbb^5 and higher under simplex, hypercubic and orthoplex groups, the latter with van Oss polytopes. There are five exceptional Lie groups: \mathfrak_2, \mathfrak_4, \mathfrak_6, \mathfrak_7, and \mathfrak_8. The smallest of these, \mathfrak_2, can be represented in five-dimensional complex space and
projected Projected is an American rock supergroup consisting of Sevendust members John Connolly and Vinnie Hornsby, Alter Bridge and Creed drummer Scott Phillips, and former Submersed and current Tremonti guitarist Eric Friedman. The band released the ...
in the same number of dimensions as a ball rolling on top of another ball, whose motion is described in two-dimensional space. \mathfrak_8, the largest of all five exceptional groups, also contains the other four as subgroups and is constructed with one hundred and twenty quaternionic unit icosians that make up the vertices of the 600-cell. There are also five solvable groups that are excluded from
finite simple group Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...
s of Lie type. The five Mathieu groups constitute the first generation in the happy family of sporadic groups. These are also the first five sporadic groups to have been described, defined as \mathrm_ multiply transitive permutation groups on n
objects Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an ai ...
, with n . In particular, \mathrm_, the smallest of all sporadic groups, has a rank 3 action on fifty-five points from an induced action on unordered pairs, as well as two five-dimensional faithful complex irreducible representations over the field with three elements, which is the lowest irreducible dimensional representation of all sporadic group over their respective fields with ''n'' elements. Of precisely five different conjugacy classes of
maximal subgroup In mathematics, the term maximal subgroup is used to mean slightly different things in different areas of algebra. In group theory, a maximal subgroup ''H'' of a group ''G'' is a proper subgroup, such that no proper subgroup ''K'' contains ''H'' ...
s of \mathrm_, one is the almost simple symmetric group \mathrm_5 (of order 5 !), and another is \mathrm_, also almost simple, that functions as a point stabilizer which has 5 as its largest prime factor in its
group order In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is ''infinite''. The ''order'' of an element of a group (also called period length or period) is the order of the sub ...
: 24·32·5 = 2·3·4·5·6 = 8·9·10 = 720. On the other hand, whereas \mathrm_ is sharply 4-transitive, \mathrm_ is sharply 5-transitive and \mathrm_ is 5-transitive, and as such they are the only two 5-transitive groups that are not symmetric groups or alternating groups. \mathrm_ has the first five prime numbers as its distinct prime factors in its order of 27· 32·5· 7· 11, and is the smallest of five sporadic groups with five distinct prime factors in their order. All Mathieu groups are subgroups of \mathrm_, which under the Witt design \mathrm_ of Steiner system S(5, 8, 24) emerges a construction of the extended binary Golay code \mathrm_ that has \mathrm_ as its automorphism group. \mathrm_ generates ''octads'' from code words of Hamming weight 8 from the extended binary Golay code, one of five different Hamming weights the extended binary Golay code uses: 0, 8, 12, 16, and 24. The Witt design and the extended binary Golay code in turn can be used to generate a faithful construction of the 24-dimensional Leech lattice Λ24, which is the subject of the second generation of seven sporadic groups that are
subquotient In the mathematical fields of category theory and abstract algebra, a subquotient is a quotient object of a subobject. Subquotients are particularly important in abelian categories, and in group theory, where they are also known as sections, thou ...
s of the automorphism of the Leech lattice, Conway group \mathrm_. There are five non-supersingular primes: 37, 43, 53, 61, and 67, all smaller than the largest of fifteen supersingular prime divisors of the friendly giant, 71.


List of basic calculations


In decimal

5 is the only prime number to end in the digit 5 in decimal because all other numbers written with a 5 in the ones place are multiples of five, which makes it a 1- automorphic number. All multiples of 5 will end in either 5 or , and vulgar fractions with 5 or in the denominator do not yield infinite decimal expansions because they are prime factors of 10, the base. In the powers of 5, every power ends with the number five, and from 53 onward, if the exponent is
odd Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric. Odd may also refer to: Acronym * ODD (Text Encoding Initiative) ("One Document Does it all"), an abstracted literate-programming format for describing X ...
, then the hundreds digit is 1, and if it is even, the hundreds digit is 6. A number n raised to the fifth power always ends in the same digit as n.


Evolution of the Arabic digit

The evolution of the modern Western digit for the numeral 5 cannot be traced back to the Indian system, as for the digits 1 to 4. The Kushana and
Gupta Gupta () is a common surname or last name of Indian origin. It is based on the Sanskrit word गोप्तृ ''goptṛ'', which means 'guardian' or 'protector'. According to historian R. C. Majumdar, the surname ''Gupta'' was adopted by sev ...
empires in what is now
India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area, the List of countries and dependencies by population, second-most populous ...
had among themselves several different forms that bear no resemblance to the modern digit. The Nagari and
Punjabi Punjabi, or Panjabi, most often refers to: * Something of, from, or related to Punjab, a region in India and Pakistan * Punjabi language * Punjabi people * Punjabi dialects and languages Punjabi may also refer to: * Punjabi (horse), a British Th ...
took these digits and all came up with forms that were similar to a lowercase "h" rotated 180°. The Ghubar Arabs transformed the digit in several different ways, producing from that were more similar to the digits 4 or 3 than to 5. It was from those digits that Europeans finally came up with the modern 5. While the shape of the character for the digit 5 has an ascender in most modern
typeface A typeface (or font family) is the design of lettering that can include variations in size, weight (e.g. bold), slope (e.g. italic), width (e.g. condensed), and so on. Each of these variations of the typeface is a font. There are thousands o ...
s, in typefaces with
text figures Text figures (also known as non-lining, lowercase, old style, ranging, hanging, medieval, billing, or antique figures or numerals) are numerals designed with varying heights in a fashion that resembles a typical line of running text, hence the ...
the glyph usually has a
descender In typography and handwriting, a descender is the portion of a letter that extends below the baseline of a font. For example, in the letter ''y'', the descender is the "tail", or that portion of the diagonal line which lies below the ''v' ...
, as, for example, in . On the
seven-segment display A seven-segment display is a form of electronic display device for displaying decimal numerals that is an alternative to the more complex dot matrix displays. Seven-segment displays are widely used in digital clocks, electronic meters, bas ...
of a calculator, it is represented by five segments at four successive turns from top to bottom, rotating counterclockwise first, then clockwise, and vice-versa.


Science

*The
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of ever ...
of boron. *The number of appendages on most starfish, which exhibit pentamerism. *The most destructive known hurricanes rate as Category 5 on the Saffir–Simpson hurricane wind scale. *The most destructive known
tornado A tornado is a violently rotating column of air that is in contact with both the surface of the Earth and a cumulonimbus cloud or, in rare cases, the base of a cumulus cloud. It is often referred to as a twister, whirlwind or cyclone, alt ...
es rate an F-5 on the Fujita scale or EF-5 on the Enhanced Fujita scale.


Astronomy

* Messier object M5, a magnitude 7.0 globular cluster in the constellation Serpens. *The New General Cataloguebr>object
NGC 5, a magnitude 13 spiral galaxy in the constellation Andromeda. *The Roman numeral V stands for dwarfs ( main sequence stars) in the Yerkes spectral classification scheme. *The Roman numeral V (usually) stands for the fifth-discovered satellite of a planet or minor planet (e.g. Jupiter V). *There are five Lagrangian points in a two-body system.


Biology

*There are generally considered to be
five senses A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of stimuli. (For example, in the human body, the brain which is part of the central nervous system rec ...
. *The five basic tastes are sweet, salty, sour, bitter, and umami. *Almost all amphibians, reptiles, and mammals which have fingers or toes have five of them on each extremity.


Computing

*5 is the
ASCII ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because ...
code of the Enquiry character, which is abbreviated to ENQ.


Religion and culture


Hinduism

*The god
Shiva Shiva (; sa, शिव, lit=The Auspicious One, Śiva ), also known as Mahadeva (; Help:IPA/Sanskrit, ɐɦaːd̪eːʋɐ, or Hara, is one of the Hindu deities, principal deities of Hinduism. He is the Supreme Being in Shaivism, one o ...
has five faces and his mantra is also called (five-worded) mantra. *The goddess Saraswati, goddess of knowledge and intellectual is associated with or the number 5. *There are five elements in the universe according to
Hindu cosmology Hindu cosmology is the description of the universe and its states of matter, cycles within time, physical structure, and effects on living entities according to Hindu texts. Hindu cosmology is also intertwined with the idea of a creator who all ...
: (earth, fire, water, air and space respectively). *The most sacred tree in Hinduism has 5 leaves in every leaf stunt. *Most of the flowers have 5 petals in them. *The epic
Mahabharata The ''Mahābhārata'' ( ; sa, महाभारतम्, ', ) is one of the two major Sanskrit epics of ancient India in Hinduism, the other being the '' Rāmāyaṇa''. It narrates the struggle between two groups of cousins in the K ...
revolves around the battle between Duryodhana and his 99 other brothers and the 5 pandava princes— Dharma, Arjuna, Bhima, Nakula and Sahadeva.


Christianity

*There are traditionally five wounds of
Jesus Christ Jesus, likely from he, יֵשׁוּעַ, translit=Yēšūaʿ, label= Hebrew/ Aramaic ( AD 30 or 33), also referred to as Jesus Christ or Jesus of Nazareth (among other names and titles), was a first-century Jewish preacher and relig ...
in
Christianity Christianity is an Abrahamic monotheistic religion based on the life and teachings of Jesus of Nazareth. It is the world's largest and most widespread religion with roughly 2.38 billion followers representing one-third of the global popula ...
: the Scourging at the Pillar, the Crowning with Thorns, the wounds in Christ's hands, the wounds in Christ's feet, and the Side Wound of Christ.


Gnosticism

*The number five was an important symbolic number in
Manichaeism Manichaeism (; in New Persian ; ) is a former major religionR. van den Broek, Wouter J. Hanegraaff ''Gnosis and Hermeticism from Antiquity to Modern Times''SUNY Press, 1998 p. 37 founded in the 3rd century AD by the Parthian prophet Mani (A ...
, with heavenly beings, concepts, and others often grouped in sets of five. * Five Seals in Sethianism * Five Trees in the Gospel of Thomas


Islam

*The Five Pillars of Islam *
Muslim Muslims ( ar, المسلمون, , ) are people who adhere to Islam, a monotheistic religion belonging to the Abrahamic tradition. They consider the Quran, the foundational religious text of Islam, to be the verbatim word of the God of Abrah ...
s pray to Allah five times a day *According to Shia Muslims, the Panjetan or the Five Holy Purified Ones are the members of
Muhammad Muhammad ( ar, مُحَمَّد;  570 – 8 June 632 CE) was an Arab religious, social, and political leader and the founder of Islam. According to Islamic doctrine, he was a prophet divinely inspired to preach and confirm the mon ...
's family:
Muhammad Muhammad ( ar, مُحَمَّد;  570 – 8 June 632 CE) was an Arab religious, social, and political leader and the founder of Islam. According to Islamic doctrine, he was a prophet divinely inspired to preach and confirm the mon ...
, Ali, Fatimah, Hasan, and Husayn and are often symbolically represented by an image of the Khamsa.


Judaism

*The
Torah The Torah (; hbo, ''Tōrā'', "Instruction", "Teaching" or "Law") is the compilation of the first five books of the Hebrew Bible, namely the books of Genesis, Exodus, Leviticus, Numbers and Deuteronomy. In that sense, Torah means the ...
contains five books—
Genesis Genesis may refer to: Bible * Book of Genesis, the first book of the biblical scriptures of both Judaism and Christianity, describing the creation of the Earth and of mankind * Genesis creation narrative, the first several chapters of the Book of ...
,
Exodus Exodus or the Exodus may refer to: Religion * Book of Exodus, second book of the Hebrew Torah and the Christian Bible * The Exodus, the biblical story of the migration of the ancient Israelites from Egypt into Canaan Historical events * E ...
, Leviticus, Numbers, and Deuteronomy—which are collectively called the Five Books of Moses, the Pentateuch ( Greek for "five containers", referring to the scroll cases in which the books were kept), or Humash (, Hebrew for "fifth"). *The book of
Psalms The Book of Psalms ( or ; he, תְּהִלִּים, , lit. "praises"), also known as the Psalms, or the Psalter, is the first book of the ("Writings"), the third section of the Tanakh, and a book of the Old Testament. The title is derived ...
is arranged into five books, paralleling the Five Books of Moses. *The Khamsa, an ancient symbol shaped like a hand with four fingers and one thumb, is used as a protective amulet by Jews; that same symbol is also very popular in
Arab The Arabs (singular: Arab; singular ar, عَرَبِيٌّ, DIN 31635: , , plural ar, عَرَب, DIN 31635: , Arabic pronunciation: ), also known as the Arab people, are an ethnic group mainly inhabiting the Arab world in Western Asia, ...
ic culture, known to protect from envy and the evil eye.


Sikhism

*The five sacred Sikh symbols prescribed by Guru Gobind Singh are commonly known as or the " Five Ks" because they start with letter K representing in the
Punjabi language Punjabi (; ; , ), sometimes spelled Panjabi, is an Indo-Aryan language of the Punjab region of Pakistan and India. It has approximately 113 million native speakers. Punjabi is the most widely-spoken first language in Pakistan, with 80.5 ...
's Gurmukhi script. They are: (unshorn hair), (the comb), (the steel bracelet), (the soldier's shorts), and (the sword) (in Gurmukhi: ). Also, there are five deadly evils: (lust), (anger), (attachment), (greed), and (ego).


Daoism

* 5 Elements * 5 Emperors


Other religions and cultures

*According to ancient Greek philosophers such as
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
, the universe is made up of five classical elements:
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
,
earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
, air,
fire Fire is the rapid oxidation of a material (the fuel) in the exothermic chemical process of combustion, releasing heat, light, and various reaction products. At a certain point in the combustion reaction, called the ignition point, flames ...
, and
ether In organic chemistry, ethers are a class of compounds that contain an ether group—an oxygen atom connected to two alkyl or aryl groups. They have the general formula , where R and R′ represent the alkyl or aryl groups. Ethers can again ...
. This concept was later adopted by medieval
alchemists Alchemy (from Arabic: ''al-kīmiyā''; from Ancient Greek: χυμεία, ''khumeía'') is an ancient branch of natural philosophy, a philosophical and protoscientific tradition that was historically practiced in China, India, the Muslim ...
and more recently by practitioners of Neo-Pagan religions such as Wicca. *The pentagram, or five-pointed star, bears religious significance in various faiths including Baháʼí,
Christianity Christianity is an Abrahamic monotheistic religion based on the life and teachings of Jesus of Nazareth. It is the world's largest and most widespread religion with roughly 2.38 billion followers representing one-third of the global popula ...
,
Freemasonry Freemasonry or Masonry refers to fraternal organisations that trace their origins to the local guilds of stonemasons that, from the end of the 13th century, regulated the qualifications of stonemasons and their interaction with authorities ...
, Satanism,
Taoism Taoism (, ) or Daoism () refers to either a school of philosophical thought (道家; ''daojia'') or to a religion (道教; ''daojiao''), both of which share ideas and concepts of Chinese origin and emphasize living in harmony with the '' Ta ...
, Thelema, and Wicca. *In
Cantonese Cantonese ( zh, t=廣東話, s=广东话, first=t, cy=Gwóngdūng wá) is a language within the Chinese (Sinitic) branch of the Sino-Tibetan languages originating from the city of Guangzhou (historically known as Canton) and its surrounding a ...
, "five" sounds like the word "not" (character: ). When five appears in front of a lucky number, e.g. "58", the result is considered unlucky. *In
East Asia East Asia is the eastern region of Asia, which is defined in both geographical and ethno-cultural terms. The modern states of East Asia include China, Japan, Mongolia, North Korea, South Korea, and Taiwan. China, North Korea, South Korea ...
n tradition, there are five elements: (
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
,
fire Fire is the rapid oxidation of a material (the fuel) in the exothermic chemical process of combustion, releasing heat, light, and various reaction products. At a certain point in the combustion reaction, called the ignition point, flames ...
,
earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
, wood, and
metal A metal (from ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, e ...
). The Japanese names for the
days of the week A day is the time period of a full rotation of the Earth with respect to the Sun. On average, this is 24 hours, 1440 minutes, or 86,400 seconds. In everyday life, the word "day" often refers to a solar day, which is the length between two ...
, Tuesday through
Saturday Saturday is the day of the week between Friday and Sunday. No later than the 2nd century, the Romans named Saturday ("Saturn's Day") for the planet Saturn, which controlled the first hour of that day, according to Vettius Valens. The da ...
, come from these elements via the identification of the elements with the five planets visible with the naked eye. Also, the traditional Japanese calendar has a five-day weekly cycle that can be still observed in printed mixed calendars combining Western, Chinese-Buddhist, and Japanese names for each weekday. *In numerology, 5 or a series of
555 Year 555 ( DLV) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. The denomination 555 for this year has been used since the early medieval period, when the Anno Domini calendar era became the p ...
, is often associated with change, evolution, love and abundance. *Members of The Nation of Gods and Earths, a primarily African American religious organization, call themselves the "Five-Percenters" because they believe that only 5% of mankind is truly enlightened.


Art, entertainment, and media


Fictional entities

* James the Red Engine, a fictional character numbered 5. * Johnny 5 is the lead character in the film ''Short Circuit'' (1986) *Number Five is a character in Lorien Legacies *Sankara Stones, five magical rocks in '' Indiana Jones and the Temple of Doom'' that are sought by the Thuggees for evil purposes *The Mach Five , the racing car Speed Racer ( in the Japanese version) drives in the anime series of the same name (known as "Mach Go! Go! Go!" in Japan) *In the works of J. R. R. Tolkien, five wizards ( Saruman, Gandalf, Radagast, Alatar and Pallando) are sent to Middle-earth to aid against the threat of the Dark Lord Sauron *In the '' A Song of Ice and Fire'' series, the War of the Five Kings is fought between different claimants to the Iron Throne of Westeros, as well as to the thrones of the individual regions of Westeros ( Joffrey Baratheon, Stannis Baratheon, Renly Baratheon, Robb Stark and Balon Greyjoy) *In '' The Wheel of Time'' series, the "Emond's Field Five" are a group of five of the series' main characters who all come from the village of Emond's Field ( Rand al'Thor, Matrim Cauthon,
Perrin Aybara This article serves as an index of major characters in the fictional setting of Robert Jordan's '' The Wheel of Time'' series, with a description of their main roles or feats in the series. ''The Wheel of Time'' has 2787 distinct named character ...
, Egwene al'Vere and Nynaeve al'Meara) * ''Myst'' uses the number 5 as a unique base counting system. In '' The Myst Reader'' series, it is further explained that the number 5 is considered a holy number in the fictional D'ni society. *Number Five is also a character in The Umbrella Academy comic book and TV series adaptation


Films

*Towards the end of the film '' Monty Python and the Holy Grail'' (1975), the character of King Arthur repeatedly confuses the number five with the number three. *'' Five Go Mad in Dorset'' (1982) was the first of the long-running series of '' The Comic Strip Presents...'' television comedy films *'' The Fifth Element'' (1997), a science fiction film * '' Fast Five'' (2011), the fifth installment of the ''Fast and Furious'' film series. *'' V for Vendetta'' (2005), produced by Warner Bros., directed by James McTeigue, and adapted from Alan Moore's graphic novel '' V for Vendetta'' prominently features number 5 and Roman Numeral V; the story is based on the historical event in which a group of men attempted to destroy Parliament on November 5, 1605


Music


Groups

* Five (group), a UK Boy band * The Five (composers), 19th-century Russian composers * 5 Seconds of Summer, pop band that originated in Sydney, Australia * Five Americans, American rock band active 1965–1969 * Five Finger Death Punch, American heavy metal band from Las Vegas, Nevada. Active 2005–present * Five Man Electrical Band, Canadian rock group billed (and active) as the Five Man Electrical Band, 1969–1975 * Maroon 5, American pop rock band that originated in Los Angeles, California * MC5, American punk rock band * Pentatonix, a Grammy-winning a cappella group originated in Arlington, Texas * The 5th Dimension, American pop vocal group, active 1977–present * The Dave Clark Five, a.k.a. DC5, an English pop rock group comprising Dave Clark, Lenny Davidson, Rick Huxley, Denis Payton, and Mike Smith; active 1958–1970 * The Jackson 5, American pop rock group featuring various members of the Jackson family; they were billed (and active) as The Jackson 5, 1966–1975 * Hi-5, Australian pop kids group, where it has several international adaptations, and several members throughout the history of the band. It was also a TV show. * We Five: American folk rock group active 1965–1967 and 1968–1977 * Grandmaster Flash and the Furious Five: American rap group, 1970–80's * Fifth Harmony, an American girl group. *
Ben Folds Five Ben Folds Five is an American alternative rock trio formed in 1993 in Chapel Hill, North Carolina. The group comprises Ben Folds (lead vocals, piano), Robert Sledge ( bass guitar, backing vocals) and Darren Jessee (drums, backing vocals). The gr ...
, an American alternative rock trio, 1993–2000, 2008 and 2011–2013 * R5 (band), an American pop and alternative rock group, 2009–2018


Other uses

*A perfect fifth is the most consonant harmony, and is the basis for most western tuning systems. *Modern musical notation uses a musical staff made of five horizontal lines. *In harmonics – the fifth
partial Partial may refer to: Mathematics *Partial derivative, derivative with respect to one of several variables of a function, with the other variables held constant ** ∂, a symbol that can denote a partial derivative, sometimes pronounced "partial d ...
(or 4th overtone) of a fundamental has a frequency ratio of 5:1 to the frequency of that fundamental. This ratio corresponds to the interval of 2 octaves plus a pure major third. Thus, the interval of 5:4 is the interval of the pure third. A major
triad Triad or triade may refer to: * a group of three Businesses and organisations * Triad (American fraternities), certain historic groupings of seminal college fraternities in North America * Triad (organized crime), a Chinese transnational orga ...
chord when played in just intonation (most often the case in a cappella vocal ensemble singing), will contain such a pure major third. *The number of completed, numbered piano concertos of
Ludwig van Beethoven Ludwig van Beethoven (baptised 17 December 177026 March 1827) was a German composer and pianist. Beethoven remains one of the most admired composers in the history of Western music; his works rank amongst the most performed of the classic ...
, Sergei Prokofiev, and Camille Saint-Saëns. *Using the Latin root, five musicians are called a quintet. *A scale with five notes per octave is called a pentatonic scale. *Five is the lowest possible number that can be the top number of a time signature with an asymmetric meter.


Television

;Stations *
Channel 5 (UK) Channel 5 is a British free-to-air public broadcast television channel launched in 1997. It is the fifth national terrestrial channel in the United Kingdom and is owned by Channel 5 Broadcasting Limited, a wholly-owned subsidiary of American ...
, a television channel that broadcasts in the United Kingdom * 5 (TV channel) (''formerly known as ABC 5 and TV5'') (
DWET-TV DWET-TV, channel 5 (analog) and channel 18 (digital), is the flagship TV station of Philippine television network TV5. The station is owned and operated by TV5 Network Inc., which is owned by MediaQuest Holdings, the multimedia arm of Phi ...
channel 5 In Metro Manila) a television network in the Philippines. ; ;Series *'' Babylon 5'', a science fiction television series *The number 5 features in the television series ''Battlestar Galactica'' in regards to the Final Five cylons and the Temple of Five * ''Hi-5'' (Australian TV series), a television series from Australia * ''Hi-5'' (UK TV series), a television show from the United Kingdom * ''Hi-5'' Philippines a television show from the Philippines *'' Odyssey 5'', a 2002 science fiction television series *'' Tillbaka till Vintergatan'', a Swedish children's television series featuring a character named "Femman" (meaning five), who can only utter the word 'five'. *'' The Five'' (talk show): Fox News Channel roundtable current events television show, premiered 2011, so-named for its panel of five commentators. *''
Yes! PreCure 5 is a Japanese anime series and the fourth installment in Izumi Todo's ''Pretty Cure'' metaseries produced by Toei Animation, featuring the third generation of Cures. The series aired on TV Asahi between February 2007 and January 2008 and ...
'' is a 2007 anime series which follows the adventures of Nozomi and her friends. It is also followed by the 2008 sequel '' Yes! Pretty Cure 5 GoGo!'' *'' The Quintessential Quintuplets'' is a 2019 slice of life romance anime series which follows the everyday life of five identical quintuplets and their interactions with their tutor. It has two seasons, and a final movie is scheduled in summer 2022. * ''Hawaii Five-0'', CBS American TV series.


Literature

* ''The Famous Five'' is a series of children's books by British writer Enid Blyton *'' The Power of Five'' is a series of children's books by British writer and screenwriter Anthony Horowitz *'' The Fall of Five'' is a book written under the collective pseudonym Pittacus Lore in the series ''Lorien Legacies'' *'' The Book of Five Rings'' is a text on kenjutsu and the martial arts in general, written by the swordsman Miyamoto Musashi circa 1645 *'' Slaughterhouse-Five'' is a book by Kurt Vonnegut about World War II


Sports

*The
Olympic Games The modern Olympic Games or Olympics (french: link=no, Jeux olympiques) are the leading international sporting events featuring summer and winter sports competitions in which thousands of athletes from around the world participate in a multi ...
have five interlocked rings as their symbol, representing the number of inhabited
continent A continent is any of several large landmasses. Generally identified by convention rather than any strict criteria, up to seven geographical regions are commonly regarded as continents. Ordered from largest in area to smallest, these seven ...
s represented by the Olympians (Europe, Asia, Africa, Australia and Oceania, and the Americas). * In AFL Women's, the top level of
women's A woman is an adult female human. Prior to adulthood, a female human is referred to as a girl (a female child or adolescent). The plural ''women'' is sometimes used in certain phrases such as "women's rights" to denote female humans regardle ...
Australian rules football, each team is allowed 5 "
interchanges Interchange may refer to: Transport * Interchange (road), a collection of ramps, exits, and entrances between two or more highways * Interchange (freight rail), the transfer of freight cars between railroad companies * Interchange station, a rai ...
" (substitute players), who can be freely substituted at any time. *In
baseball scorekeeping Baseball scorekeeping is the practice of recording the details of a baseball game as it unfolds. Professional baseball leagues hire official scorers to keep an official record of each game (from which a box score can be generated), but many fans ...
, the number 5 represents the
third baseman A third baseman, abbreviated 3B, is the player in baseball or softball whose responsibility is to defend the area nearest to third base — the third of four bases a baserunner must touch in succession to score a run. In the scoring system u ...
's position. *In
basketball Basketball is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular Basketball court, court, compete with the primary objective of #Shooting, shooting a basketball (ball), basketball (appr ...
: **The number 5 is used to represent the position of center. **Each team has five players on the court at a given time. Thus, the phrase "five on five" is commonly used to describe standard competitive basketball. **The "5-second rule" refers to several related rules designed to promote continuous play. In all cases, violation of the rule results in a turnover. **Under the FIBA (used for all international play, and most non-US leagues) and NCAA women's rule sets, a team begins shooting bonus free throws once its opponent has committed five personal fouls in a quarter. **Under the FIBA rules, A player fouls out and must leave the game after committing five fouls * Five-a-side football is a variation of
association football Association football, more commonly known as football or soccer, is a team sport played between two teams of 11 players who primarily use their feet to propel the ball around a rectangular field called a pitch. The objective of the game is ...
in which each team fields five players. *In
ice hockey Ice hockey (or simply hockey) is a team sport played on ice skates, usually on an ice skating rink with lines and markings specific to the sport. It belongs to a family of sports called hockey. In ice hockey, two opposing teams use ice ...
: ** A major penalty lasts five minutes. ** There are five different ways that a player can score a goal (teams at even strength, team on the power play, team playing shorthanded, penalty shot, and empty net). ** The area between the goaltender's legs is known as the five-hole. *In most
rugby league Rugby league football, commonly known as just rugby league and sometimes football, footy, rugby or league, is a full-contact sport played by two teams of thirteen players on a rectangular field measuring 68 metres (75 yards) wide and 112 ...
competitions, the starting left wing wears this number. An exception is the Super League, which uses static squad numbering. *In
rugby union Rugby union, commonly known simply as rugby, is a close-contact team sport that originated at Rugby School in the first half of the 19th century. One of the two codes of rugby football, it is based on running with the ball in hand. In it ...
: ** A try is worth 5 points. ** One of the two starting lock forwards wears number 5, and usually jumps at number 4 in the line-out. ** In the French variation of the bonus points system, a bonus point in the league standings is awarded to a team that loses by 5 or fewer points.


Technology

*5 is the most common number of gears for automobiles with
manual transmission A manual transmission (MT), also known as manual gearbox, standard transmission (in Canada, the United Kingdom, and the United States), or stick shift (in the United States), is a multi-speed motor vehicle transmission (mechanics), transmission ...
. *In radio communication, the term " Five by five" is used to indicate perfect signal strength and clarity. *On almost all devices with a numeric keypad such as telephones, computers, etc., the 5 key has a raised dot or raised bar to make dialing easier. Persons who are blind or have low vision find it useful to be able to feel the keys of a telephone. All other numbers can be found with their relative position around the 5 button (on computer keyboards, the 5 key of the numpad has the raised dot or bar, but the 5 key that shifts with % does not). *On most telephones, the 5 key is associated with the letters J, K, and L, but on some of the BlackBerry phones, it is the key for G and H. *The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture
microprocessor A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit, or a small number of integrated circuits. The microprocessor contains the arithmetic, logic, and control circ ...
. *The resin identification code used in recycling to identify
polypropylene Polypropylene (PP), also known as polypropene, is a thermoplastic polymer used in a wide variety of applications. It is produced via chain-growth polymerization from the monomer propylene. Polypropylene belongs to the group of polyolefins a ...
.


Miscellaneous fields

Five can refer to: *"Give me five" is a common phrase used preceding a high five. *An informal term for the British Security Service, MI5. *Five babies born at one time are quintuplets. The most famous set of quintuplets were the
Dionne quintuplets The Dionne quintuplets (; born May 28, 1934) are the first quintuplets known to have survived their infancy. The identical girls were born just outside Callander, Ontario, near the village of Corbeil. All five survived to adulthood. The Di ...
born in the 1930s. *In the United States legal system, the
Fifth Amendment to the United States Constitution The Fifth Amendment (Amendment V) to the United States Constitution addresses criminal procedure and other aspects of the Constitution. It was ratified, along with nine other articles, in 1791 as part of the Bill of Rights. The Fifth Amen ...
can be referred to in court as "pleading the fifth", absolving the defendant from
self-incrimination In criminal law, self-incrimination is the act of exposing oneself generally, by making a statement, "to an accusation or charge of crime; to involve oneself or another ersonin a criminal prosecution or the danger thereof". (Self-incriminati ...
. * Pentameter is verse with five repeating feet per line; iambic pentameter was the most popular form in
Shakespeare William Shakespeare ( 26 April 1564 – 23 April 1616) was an English playwright, poet and actor. He is widely regarded as the greatest writer in the English language and the world's pre-eminent dramatist. He is often called England's nation ...
. *
Quintessence Quintessence, or fifth essence, may refer to: Cosmology * Aether (classical element), in medieval cosmology and science, the fifth element that fills the universe beyond the terrestrial sphere * Quintessence (physics), a hypothetical form of da ...
, meaning "fifth element", refers to the elusive fifth element that completes the basic four elements (water, fire, air, and earth) *The designation of an Interstate Highway ( Interstate 5) that runs from
San Diego San Diego ( , ; ) is a city on the Pacific Ocean coast of Southern California located immediately adjacent to the Mexico–United States border. With a 2020 population of 1,386,932, it is the eighth most populous city in the United States ...
,
California California is a state in the Western United States, located along the Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the most populous U.S. state and the 3rd largest by area. It is also the m ...
to Blaine, Washington. In addition, all major north-south Interstate Highways in the United States end in 5. *In the computer game ''
Riven ''Riven'' is a puzzle adventure video game. It is the sequel to '' Myst'' and second in the ''Myst'' series of games. Developed by Cyan Worlds, it was initially published by Red Orb Entertainment, a division of Broderbund. ''Riven'' was distri ...
'', 5 is considered a holy number, and is a recurring theme throughout the game, appearing in hundreds of places, from the number of islands in the game to the number of bolts on pieces of machinery. *''
The Garden of Cyrus ''The Garden of Cyrus'', or ''The Quincuncial Lozenge, or Network Plantations of the Ancients, naturally, artificially, mystically considered'', is a discourse by Sir Thomas Browne. First published in 1658, along with its diptych companion '' Ur ...
'' (1658) by Sir Thomas Browne is a Pythagorean discourse based upon the number 5. *The holy number of Discordianism, as dictated by the Law of Fives. *The number of Justices on the
Supreme Court of the United States The Supreme Court of the United States (SCOTUS) is the highest court in the federal judiciary of the United States. It has ultimate appellate jurisdiction over all U.S. Federal tribunals in the United States, federal court cases, and over Stat ...
necessary to render a majority decision. *The number of dots in a quincunx. *The number of permanent members with veto power on the
United Nations Security Council The United Nations Security Council (UNSC) is one of the six principal organs of the United Nations (UN) and is charged with ensuring international peace and security, recommending the admission of new UN members to the General Assembly, ...
. *The number of sides and the number of angles in a pentagon. *The number of points in a pentagram. *The number of Korotkoff sounds when measuring blood pressure *The drink Five Alive is named for its five ingredients. The drink
punch Punch commonly refers to: * Punch (combat), a strike made using the hand closed into a fist * Punch (drink), a wide assortment of drinks, non-alcoholic or alcoholic, generally containing fruit or fruit juice Punch may also refer to: Places * Pu ...
derives its name after the Sanskrit पञ्च (pañc) for having five ingredients. *The Keating Five were five
United States Senators The United States Senate is the upper chamber of the United States Congress, with the House of Representatives being the lower chamber. Together they compose the national bicameral legislature of the United States. The composition and p ...
accused of corruption in 1989. *The
Inferior Five The Inferior Five (or I5) are a parody superhero team appearing in books by the American publisher DC Comics. Created by writer E. Nelson Bridwell and artist Joe Orlando, the team premiered in the DC Comics title ''Showcase'' #62 (May-June 19 ...
: Merryman, Awkwardman, The Blimp, White Feather, and Dumb Bunny.
DC Comics DC Comics, Inc. ( doing business as DC) is an American comic book publisher and the flagship unit of DC Entertainment, a subsidiary of Warner Bros. Discovery. DC Comics is one of the largest and oldest American comic book companies, with the ...
parody superhero team. * No. 5 is the name of the iconic fragrance created by Coco Chanel. *The Committee of Five was delegated to draft the
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental United States, primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., ...
Declaration of Independence. *The five-second rule is a commonly used rule of thumb for dropped food. *555 95472, usually referred to simply as 5, is a minor male character in the comic strip ''Peanuts''.


See also

* Five Families * Five Nations (disambiguation) * 555 (number) * List of highways numbered 5


References

*Wells, D. '' The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 58–67


External links

* *
The Number 5The Positive Integer 5
{{DEFAULTSORT:5 (Number) Integers 5 (number)