To divide 15 by \( \frac{5}{8} \), you can multiply 15 by the reciprocal of \( \frac{5}{8} \). The reciprocal of \( \frac{5}{8} \) is \( \frac{8}{5} \).
So, the calculation becomes:
\[ 15 \div \frac{5}{8} = 15 \times \frac{8}{5} \]
Now, perform the multiplication:
\[ = \frac{15 \times 8}{5} = \frac{120}{5} = 24 \]
Therefore, the quotient of \( 15 \div \frac{5}{8} \) is 24.