To divide two fractions, you multiply the first fraction by the reciprocal of the second fraction.
So, to divide \(-\frac{5}{8}\) by \(-\frac{2}{3}\), we first find the reciprocal of \(-\frac{2}{3}\), which is \(-\frac{3}{2}\).
Now, we can write the expression as follows:
\[ -\frac{5}{8} \div -\frac{2}{3} = -\frac{5}{8} \times -\frac{3}{2} \]
When we multiply two negative fractions, the result is positive:
\[ \frac{5 \times 3}{8 \times 2} = \frac{15}{16} \]
Therefore, the quotient of \(-\frac{5}{8} \div -\frac{2}{3}\) is \(\frac{15}{16}\).