Five is the third prime number. Because it can be written as 2^2¹ + 1, five is classified as a Fermat prime; therefore a regular polygon with 5 sides (a regular pentagon) is constructible with compass and unmarked straightedge. 5 is the third Sophie Germain prime, the first safe prime, the third Catalan number, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. Five is the first good prime. It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. It is also the only number that is part of more than one pair of twin primes. Five is a congruent number.

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.

...
Wikipedia