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Algebra Level 4

\[\huge \sqrt[5x]{{\left( \sqrt[x^5]{{(5)}^5}\right)}^{\sqrt[5]{x}}} = 3125\]
Find the real value of \(x\) satisfying the real equation above.

The answer is of the form \(5^{-\dfrac{a}{b}}\), where \(a\) and \(b\) are positive co-prime integers, then find the value of \(a + b\).

\(\text{Note}\):- Here \(x \neq \{-1 , 0 , 1\}\)

This is one part of the set Fun with exponents

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