5^an constant mod 100000?

25125(mod1000)252625(mod1000)253625(mod1000)254625(mod1000) \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 25n 25 ^ n will always be a constant 625 for large enough integer values of n n .

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

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