\[f(x) = \sqrt{x + 5\ } + \sqrt{3 - x\ }\ \]
\[\left\{ \begin{matrix} x + 5 \geq 0 \\ 3 - x \geq 0 \\ \end{matrix}\text{\ \ \ \ \ \ \ } \right.\ \left\{ \begin{matrix} x \geq - 5 \\ x \leq 3\ \ \ \\ \end{matrix} \right.\ \]
\[\Longrightarrow \lbrack - 5;3\rbrack.\]