Five (5) is a positive integer one more than 4 and one less than 6.
5 is the third prime number (between 3 and 7). It is a Mersenne prime exponent (producing 31), and a Fermat prime (between 3 and 17).
5 is the second square pyramidal number (between 1 and 14), and the second pentatope number (between 1 and 15).
5 is the only number to be twin primes with two numbers. It forms pairs with both 3 and 7.
5 is the fifth term of the Fibonacci sequence, between 3 and 8.
5 is half of 10, our number base, and is the number of fingers on one hand.
5 is an odd prime number. Since 10 is a multiple of 5, divisibility by 5 can be easily tested in the decimal system — multiples of 5 always end in 0 or 5. 5 is a Fermat prime: 221 + 1 = 5.
A 5-sided star is known as a pentagram.
In googology Edit
Some googologisms based on 5 are superpent, googolquinplex and quintoogol. 5 is the length of the Goodstein sequence starting with 3, which goes 3, 3, 3, 2, 1.
In Greek-based number naming systems, 5 is associated with prefix penta-, and with prefix quint- in Latin systems.
Donald Knuth calls this number quintiad, and it's equal to using the -yllion system
Related to this, to test if a number is divisible by 5, all you need to do is check the last digit. If it is 0 or 5, the number is divisible by 5.