Answer
$\dfrac{5\sqrt[3]{4x}}{2x}$
Work Step by Step
Multiplying both the numerator and the denominator by $
\sqrt[3]{4x}
$, then the rationalized-denominator form of the given expression, $
\dfrac{5}{\sqrt[3]{2x^2}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{5}{\sqrt[3]{2x^2}}\cdot\dfrac{\sqrt[3]{4x}}{\sqrt[3]{4x}}
\\\\=
\dfrac{5\sqrt[3]{4x}}{\sqrt[3]{8x^3}}
\\\\=
\dfrac{5\sqrt[3]{4x}}{\sqrt[3]{(2x)^3}}
\\\\=
\dfrac{5\sqrt[3]{4x}}{2x}
.\end{array}