Simplify cube root of 5* cube root of 5^5

$\sqrt[3]{5} \cdot \sqrt[3]{5^{5}}$

Combine using the product rule for radicals.

$\sqrt[3]{5 \cdot 5^{5}}$

Multiply $5$ by $5^{5}$ by adding the exponents.

Multiply $5$ by $5^{5}$ .

Raise $5$ to the power of $1$ .

$\sqrt[3]{5^{1} \cdot 5^{5}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[3]{5^{1 + 5}}$

Add $1$ and $5$ .

$\sqrt[3]{5^{6}}$

Raise $5$ to the power of $6$ .

$\sqrt[3]{15625}$

Rewrite $15625$ as $25^{3}$ .

$\sqrt[3]{25^{3}}$

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

$25$