#### Answer

$\dfrac{5\sqrt[3]{2}}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the denominator of the given expression, $
\dfrac{5}{\sqrt[3]{4}}
,$ multiply by an expression equal to $1$ which will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying the given expression by an expression equal to $1$ which will make the denominator a perfect power of the index and then simplifying the radical result to
\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]{8}}
\\\\=
\dfrac{5\sqrt[3]{2}}{\sqrt[3]{(2)^3}}
\\\\=
\dfrac{5\sqrt[3]{2}}{2}
.\end{array}