This is my first post. I am practicing simple congruence theory to solve divisibility problems.

For example, to show $\displaystyle 13\mid3^{n+2}+4^{2n+1}$:

$\displaystyle 3^n3^2+(4^2)^n4 \bmod 13 \equiv 3^n9+3^n4 \equiv 3^n(9+4) \equiv 3^n(13) \equiv 3^n(0) \equiv 0 \bmod 13$, which is what we set out to prove.

This works very well for all the problems I've been working on, but there is one with a minus sign that is throwing me off:

Show: $\displaystyle 7\mid5^{2n}+3\cdot2^{5n-2}$.

Any suggestions?