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.