/sci/ - Science & Math

I'm trying to prove by induction that 7^n-2^n is divisable by 5, for all natural numbers n.

The first step is fine:

f(1) = 7^1-2^1 = 5 (divisable by 5)

The second step, I can't work out. This is as far as a got:

f(n+1) = 7^(n+1)-2^(n+1)
= 7*7^n-2*2^n
= 5((7/5)*7^n-(2/5)*2^n)
= 5((35*7^n-10*2^n)/25)

Can anyone help me out?