$$a_{n+1}=5 ^n a_n$$

Calculus Level 2

The sequence $$\{a_n\}$$ satisfies $$a_1=1$$ and $a_{n+1}=5 ^n a_n \text{ for } n \geq 1.$

For what value of $$k$$ do we have $$a_k=5 ^{276}$$?

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