All powers of 5 end in 5

I think that needs a tiny proof. I would use induction but maybe it can be done simpler.

f(k) = 5^k for k=1 ends in a 5.
assume f(n) ends in a 5
then f(n+1) ends in a 5 since f(n+1) = 5 * f(n) with the final digit of f(n) ending in a 5.

But perhaps I am overcomplicating stuff.