Answer
$\dfrac{5\sqrt{y}}{y^3}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt{\dfrac{25}{y^5}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{25}{y^4}\cdot\dfrac{1}{y}}
\\\\=
\sqrt{\left( \dfrac{5}{y^2}\right)^2\cdot\dfrac{1}{y}}
\\\\=
\dfrac{5}{y^2}\sqrt{\dfrac{1}{y}}
\\\\=
\dfrac{5}{y^2}\sqrt{\dfrac{1}{y}\cdot\dfrac{y}{y}}
\\\\=
\dfrac{5}{y^2}\sqrt{\dfrac{y}{y^2}}
\\\\=
\dfrac{5}{y^2}\cdot\dfrac{\sqrt{y}}{\sqrt{y^2}}
\\\\=
\dfrac{5}{y^2}\cdot\dfrac{\sqrt{y}}{y}
\\\\=
\dfrac{5\sqrt{y}}{y^3}
.\end{array}
Note that all variables are assumed to represent positive real numbers.