To find the quotient of \(-\frac{5}{8} \div -\frac{2}{3}\), you can rewrite the division as multiplication by the reciprocal of the divisor.
So, we have:
\[ -\frac{5}{8} \div -\frac{2}{3} = -\frac{5}{8} \times -\frac{3}{2} \]
Next, multiply the numerators and the denominators:
\[ = \frac{5 \times 3}{8 \times 2} \]
Calculating the numerator and denominator, we get:
\[ = \frac{15}{16} \]
Thus, the quotient of \(-\frac{5}{8} \div -\frac{2}{3}\) is \(\frac{15}{16}\).