To divide fractions, we multiply by the reciprocal of the second fraction. So, we have:
$\dfrac{9}{7} \div \left(-\dfrac{9}{5}\right) = \dfrac{9}{7} \cdot \left(-\dfrac{5}{9}\right)$
We can cancel the common factors of 9:
$= \dfrac{1}{7} \cdot \left(-\dfrac{5}{1}\right)$
$= \dfrac{-5}{7}$
The answer, in simplest form, is $\boxed{-\dfrac{5}{7}}$.