#### Answer

$15\sqrt[3]{5}$

#### Work Step by Step

Extracting the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[3]{5000}+\sqrt[3]{625}
\\\\=
\sqrt[3]{1000\cdot5}+\sqrt[3]{125\cdot5}
\\\\=
\sqrt[3]{(10)^3\cdot5}+\sqrt[3]{(5)^3\cdot5}
\\\\=
10\sqrt[3]{5}+5\sqrt[3]{5}
\\\\=
15\sqrt[3]{5}
.\end{array}