To multiply the fractions \( \frac{5}{8} \) and \( \frac{3}{11} \), you multiply the numerators together and the denominators together:
\[ \frac{5}{8} \times \frac{3}{11} = \frac{5 \times 3}{8 \times 11} = \frac{15}{88} \]
So, \( \frac{5}{8} \times \frac{3}{11} = \frac{15}{88} \).