Prove that $\displaystyle 7|5^{2n}+(3)(2^{5n-2})$

I tried to use induction on this one. The statement is true for n = 1, assume k is true.

I have $\displaystyle 5^{2k+2}+3(2^{5k+3})$

Then $\displaystyle 5^{2k}(25)+3(2^{5k-2})(32) \equiv 5^{2k}(4)+3(2^{5k-2})(4) \equiv 0 \ (mod \ 7)$

This right?