Primality proof for n = 5:
Take b = 2.
b^(n-1) mod n = 1.
2 is prime. b^((n-1)/2)-1 mod n = 3, which is a unit, inverse 2.
(2^2) divides n-1.
(2^2)^2 > n.
n is prime by Pocklington's theorem.