Simplify cube root of 64(a-5)^5

$\sqrt[3]{64 {(a - 5)}^{5}}$

Rewrite $64 {(a - 5)}^{5}$ as ${(4 (a - 5))}^{3} {(a - 5)}^{2}$ .

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{4^{3} {(a - 5)}^{5}}$

Factor out ${(a - 5)}^{3}$ .

$\sqrt[3]{4^{3} ({(a - 5)}^{3} {(a - 5)}^{2})}$

Rewrite $4^{3} {(a - 5)}^{3}$ as ${(4 (a - 5))}^{3}$ .

$\sqrt[3]{{(4 (a - 5))}^{3} {(a - 5)}^{2}}$

Pull terms out from under the radical.

$4 (a - 5) \sqrt[3]{{(a - 5)}^{2}}$