Answer
$\dfrac{5\sqrt[3]{2}}{3}$
Work Step by Step
Multiplying both the numerator and the denominator by a factor that will make the denominator a perfect power of the radical, the rationalized-denominator form of the given expression, $
\dfrac{5}{\sqrt[3]{4}}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{5}{\sqrt[3]{4}}\cdot\dfrac{\sqrt[3]{2}}{\sqrt[3]{2}}
\\\\=
\dfrac{5\sqrt[3]{2}}{\sqrt[3]{4(2)}}
\\\\=
\dfrac{5\sqrt[3]{2}}{\sqrt[3]{(2)^3}}
\\\\=
\dfrac{5\sqrt[3]{2}}{3}
.\end{array}
