5^n - 2 divisible by 3

When n = 1, 5^n - 2 = 3 Divisible by 3

n = 2, 5^2 - 2 = 23 (not divisible by 3)

n = 3 5^3 - 2 = 123 (divisible by 3)

n = 4 5^4 - 2 = 623 (not divisible)

n = 5 5^5 - 2 = 3123 (divisible)

n = 6 5^6 - 2 = 15623 (not divisible)

Looks like 5^n - 2 is divisible by 3 only if n is odd.