Answer
$\dfrac{5}{\sqrt[3]{100}}$
Work Step by Step
Rationalizing the numerator, the given expression, $
\dfrac{\sqrt[3]{5}}{\sqrt[3]{4}}
,$ is equivalent to
\begin{array}{l}
\dfrac{\sqrt[3]{5}}{\sqrt[3]{4}}\cdot\dfrac{\sqrt[3]{5^2}}{\sqrt[3]{5^2}}
\\\\=
\dfrac{\sqrt[3]{5^3}}{\sqrt[3]{4\cdot25}}
\\\\=
\dfrac{5}{\sqrt[3]{100}}
.\end{array}