Answer
$\dfrac{x-25}{-3\sqrt[]{x}+15}$
Work Step by Step
Multiplying by the conjugate of the numerator, the rationalized-numerator form of the given expression, $
\dfrac{\sqrt[]{x}+5}{-3}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[]{x}+5}{-3}\cdot\dfrac{\sqrt[]{x}-5}{\sqrt[]{x}-5}
\\\\=
\dfrac{(\sqrt[]{x})^2-(5)^2}{-3\sqrt[]{x}+15}
\\\\=
\dfrac{x-25}{-3\sqrt[]{x}+15}
.\end{array}
Note that all variables are assumed to have positive real numbers.