# 5^an constant mod 100000?

$\begin{array} { l c c } 25 ^ 1 & \equiv 25 & \pmod{1000} \\ 25 ^ 2 & \equiv 625 & \pmod{1000} \\ 25 ^ 3 & \equiv 625 & \pmod{1000} \\ 25 ^ 4 & \equiv 625 & \pmod{1000} \\ \vdots & \vdots & \vdots \\ \end{array}$

We know that the last 3 digits of $$25 ^ n$$ will always be a constant 625 for large enough integer values of $$n$$.

What is the smallest positive integer value $$a$$ such that the last 5 digits of $$\left( 5 ^ a \right) ^n$$ will always be a constant for large enough integer values of $$n$$?

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