\[f(x) = \sqrt{x + 5} + \frac{6}{x^{2} - 4}\]
\[\left\{ \begin{matrix} x + 5 \geq 0\ \\ x² - 4 \neq 0 \\ \end{matrix} \right.\ \ \Longrightarrow \left\{ \begin{matrix} x \geq - 5 \\ x² \neq 4\ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x \geq - 5 \\ x \neq \pm 2 \\ \end{matrix} \right.\ \]
\[D(f) = \lbrack - 5;\ - 2) \cup ( - 2;2) \cup (2;\ + \infty).\]