5

Definition
$5$ (Five) is:


 * The second pentagonal number:
 * $5 = 1 + 4$


 * The length of the hypotenuse of the smallest Pythagorean triangle:
 * $3 - 4 - 5$ triangle


 * The second automorphic number after $1$:
 * $5^2 = 2 \mathbf 5$


 * The smallest prime number of the form $4 n + 1$, and thus, from Fermat's Two Squares Theorem, the sum of two squares uniquely:
 * $5 = 4 \times 1 + 1 = 2^2 + 1^2$


 * The smallest prime number of the form $6 n - 1$:
 * $5 = 6 \times 1 - 1$


 * The second Fermat number, and thus Fermat prime, after $3$:
 * $5 = 2^{\left({2^1}\right)} + 1$


 * The only member of $2$ pairs of twin primes:
 * $\left({3, 5}\right)$ and $\left({5, 7}\right)$


 * The first of the smallest sequence of both $4$ and $5$ prime numbers in arithmetic progression;
 * $5, 11, 17, 23$
 * $5, 11, 17, 23, 29$


 * Probably the only odd untouchable number.