Simplify fourth root of (-5)^4

$\sqrt[4]{{(- 5)}^{4}}$

Raise $- 5$ to the power of $4$ .

$\sqrt[4]{625}$

Rewrite $625$ as $5^{4}$ .

$\sqrt[4]{5^{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$5$