Let's denote the unknown number as \( x \). According to the information given:
\[ \frac{3}{5} x = 24 \]
To find \( x \), we can multiply both sides by \( \frac{5}{3} \):
\[ x = 24 \times \frac{5}{3} \]
Calculating the right side:
\[ x = 24 \times \frac{5}{3} = 24 \times \frac{5}{3} = \frac{120}{3} = 40 \]
Now that we've found \( x = 40 \), we want to calculate \( \frac{5}{8} \) of the number:
\[ \frac{5}{8} x = \frac{5}{8} \times 40 \]
Calculating this:
\[ \frac{5 \times 40}{8} = \frac{200}{8} = 25 \]
Thus, \( \frac{5}{8} \) of the number is \( 25 \).
The answer is \( A) 25 \).