Answer
$\dfrac{11y\sqrt[3]{y^2}}{8}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\dfrac{\sqrt[3]{y^5}}{8}+\dfrac{5y\sqrt[3]{y^2}}{4}
\\\\=
\dfrac{\sqrt[3]{y^3\cdot y^2}}{8}+\dfrac{5y\sqrt[3]{y^2}}{4}
\\\\=
\dfrac{y\sqrt[3]{y^2}}{8}+\dfrac{5y\sqrt[3]{y^2}}{4}
\\\\=
\dfrac{y\sqrt[3]{y^2}+2(5y\sqrt[3]{y^2})}{8}
\\\\=
\dfrac{y\sqrt[3]{y^2}+10y\sqrt[3]{y^2}}{8}
\\\\=
\dfrac{11y\sqrt[3]{y^2}}{8}
.\end{array}
