To find the quotient of \(-\frac{5}{8} \div -\frac{2}{3}\), we first remember that dividing by a fraction is the same as multiplying by its reciprocal. Thus, we can rewrite the expression:
\[ -\frac{5}{8} \div -\frac{2}{3} = -\frac{5}{8} \times -\frac{3}{2} \]
Now, multiplying the fractions:
\[ -\frac{5}{8} \times -\frac{3}{2} = \frac{5 \times 3}{8 \times 2} = \frac{15}{16} \]
So the quotient of \(-\frac{5}{8} \div -\frac{2}{3}\) is:
\[ \frac{15}{16} \]