Prove that for all $\displaystyle n \geq 1$, prove $\displaystyle 5$ divides $\displaystyle 8^n - 3^n$ using inducation.

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So I know the inductive step:

Assume $\displaystyle 5$ divides $\displaystyle 8^k-3^k$

Show $\displaystyle 5$ divides $\displaystyle 8^{k+1} - 3^{k+1}$

So, $\displaystyle 8^k - 3^k = 5p$, for some integer $\displaystyle p$. This is the inductive hypothesis.

$\displaystyle 8^{k+1}-3^{k+1} = \left(8^k\cdot 8 - 3^k\cdot 3\right) = \left(8^k\cdot (5+3) - 3^k\cdot 3\right) = \left(5\cdot 8^k + 3\cdot 8^k\right) - 3^k\cdot 3$

I'm stuck from here. Thanks for the help.