To divide two fractions, you can multiply the first fraction by the reciprocal of the second fraction.
Given the expression:
\[ -\frac{5}{8} \div -\frac{2}{3} \]
This can be rewritten as:
\[ -\frac{5}{8} \times -\frac{3}{2} \]
Now, multiplying the two fractions:
\[ \frac{5 \times 3}{8 \times 2} = \frac{15}{16} \]
Since both signs were negative, the result is positive. Thus, the quotient of \(-\frac{5}{8} \div -\frac{2}{3}\) is:
\[ \frac{15}{16} \]