\[\frac{5a - 15}{a + 1}\ :\frac{a^{2} - 9}{a^{2} - 1} = \frac{(5a - 15) \cdot (a^{2} - 1)}{(a + 1) \cdot (a^{2} - 9)} =\]
\[= \frac{5 \cdot (a - 3)(a - 1)(a + 1)}{(a + 1)(a - 3)(a + 3)} = \frac{5 \cdot (a - 1)}{a + 3} =\]
\[= \frac{5a - 5}{a + 3}\]