#### Answer

$\dfrac{5a^2\sqrt[]{a}}{b^3}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt[]{\dfrac{25a^5}{b^6}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[]{25a^5}}{\sqrt[]{b^6}}
\\\\=
\dfrac{\sqrt[]{25a^4\cdot a}}{\sqrt[]{b^6}}
\\\\=
\dfrac{\sqrt[]{(5a^2)^2\cdot a}}{\sqrt[]{(b^3)^2}}
\\\\=
\dfrac{5a^2\sqrt[]{a}}{b^3}
\end{array}
* Note that it is assumed that all variables represent positive numbers.