Prove that $\displaystyle 2222^{5555}+5555^{2222}$ is divisible by 7.

I set about trying to show that this expression is equal to $\displaystyle 0 \mod 7$.

I have that:

$\displaystyle 2222=3 \mod7=2 \mod 6$

$\displaystyle 5555=4 \mod 7=5 \mod 6$

The question also has Fermat's little theorem above it so I think I should be using that somewhere.

Anyone have any ideas?