To find the product of \( \frac{5}{8} \) and \( \frac{3}{4} \), you multiply the numerators together and the denominators together:
\[ \frac{5}{8} \times \frac{3}{4} = \frac{5 \times 3}{8 \times 4} = \frac{15}{32} \]
Therefore, the correct answer is \( \frac{15}{32} \).