Answer
$-\frac{1}{a}$
Work Step by Step
We know that $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}}=a^{n}$ (as long as a is a nonzero real number and n is an integer).
Therefore, $\frac{15a^{4}}{-15a^{5}}=\frac{15}{-15}\times a^{4-5}=-1\times a^{-1}=-1\times\frac{1}{a}=-\frac{1}{a}$.