Answer
$$ -5\sqrt 3$$
Work Step by Step
Recall that the definition $\sqrt{-a} = i\sqrt{a}$ must be applied BEFORE the other rules regarding radicals, therefore,
$\sqrt {-5}*\sqrt {-15} = i\sqrt {5}* i\sqrt {15} $
$i^2\sqrt{75}$
$(-1)(5\sqrt{3})$
$$-5\sqrt 3$$