5^an constant mod 100000?

Number Theory Level 4

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

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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