5

5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has garnered attention throughout history in part because distal extremities in humans typically contain five digits.

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 empires in what is now India had among themselves several forms that bear no resemblance to the modern digit. The Nagari and Punjabi 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 ways, producing from that were more similar to the digits 4 or 3 than to 5.^[1] 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 typefaces, in typefaces with text figures the glyph usually has a descender, as, for example, in .

On the seven-segment display 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.

${\displaystyle 5}$ is the third smallest prime number, and the second super-prime.^[2] It is the first safe prime,^[3] the first good prime,^[4] the first balanced prime,^[5] and the first of three known Wilson primes.^[6] Five is the second Fermat prime^[2] and the third Mersenne prime exponent,^[7] as well as the third Catalan number,^[8] and the third Sophie Germain prime.^[2] 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).^[9][10] It also forms the first pair of sexy primes with 11,^[11] which is the fifth prime number and first repunit prime in decimal; a base in-which five is also the first non-trivial 1-automorphic number.^[12] Five is the third factorial prime,^[13] an alternating factorial,^[14] and an Eisenstein prime with no imaginary part and real part of the form .^[2] In particular, five is the first congruent number, since it is the length of the hypotenuse of the smallest integer-sided right triangle.^[15]${\displaystyle 3p-1}$

Five is the second Fermat prime of the form , and more generally the second Sierpiński number of the first kind, .^[16] There are a total of five known Fermat primes, which also include 3, 17, 257, and 65537.^[17] The sum of the first three Fermat primes, 3, 5 and 17, yields 25 or 5², while 257 is the 55th prime number. Combinations from these five Fermat primes generate 31 polygons with an odd number of sides that can be ${\displaystyle 2^{2^{n}}+1}$${\displaystyle n^{n}+1}$constructed purely with a compass and straight-edge, which includes the five-sided regular pentagon.^[18][19] Apropos, 31 is also equal to the sum of the maximum number of areas inside a circle that are formed from the sides and diagonals of the first five -sided polygons, which is equal to the maximum number of areas formed by a six-sided polygon; per Moser's circle problem.^[20]${\displaystyle n}$

The first Pythagorean triple, with a hypotenuse of ${\displaystyle 5}$

The smallest non-trivial magic square

Illustration by Leonardo da Vinci of a regular dodecahedron, from Luca Pacioli's Divina proportione

The five sensory organ modalities, with touch represented by the hand's tactility

International maritime signal flag for 5

The fives of all four suits in playing cards