\[\frac{x^{2} - 16}{3 - \sqrt{x + 5}} =\]
\[= \frac{(x - 4)(x + 4)\left( 3 + \sqrt{x + 5} \right)}{\left( 3 - \sqrt{x + 5} \right)\left( 3 + \sqrt{x + 5} \right)} =\]
\[= \frac{(x - 4)(x + 4)\left( 3 + \sqrt{x + 5} \right)}{9 - (x + 5)} =\]
\[= \frac{(x - 4)(x + 4)\left( 3 + \sqrt{x + 5} \right)}{9 - x - 5} =\]
\[= - (x + 4)(3 + \sqrt{x + 5})\]