Recurring Theme, Part $$n+1$$

Algebra Level 5

If $$a_1=10, a_2=6$$ and $$5a_{n+2}=6a_{n+1}-5a_n$$ for $$n>0$$, find the maximal value of $$a_n$$, for all positive integers $$n$$.

If you come to the conclusion that no such maximum exists, enter 666.

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