Answer
The simplified form of $\sqrt{x+5}\sqrt[5]{x+5}$ is ${{\left( x+5 \right)}^{\frac{7}{10}}}$.
Work Step by Step
Consider the expression.
$\sqrt{x+5}\sqrt[5]{x+5}$
Simplified as follows,
$\sqrt{x+5}\sqrt[5]{x+5}={{\left( x+5 \right)}^{\frac{1}{2}}}{{\left( x+5 \right)}^{\frac{1}{5}}}$
Apply the product rule of exponents.
$\begin{align}
& \sqrt{x+5}\sqrt[5]{x+5}={{\left( x+5 \right)}^{\frac{1}{2}+\frac{1}{5}}} \\
& ={{\left( x+5 \right)}^{\frac{5+2}{10}}} \\
& ={{\left( x+5 \right)}^{\frac{7}{10}}}
\end{align}$
