To multiply the fractions \( \frac{5}{3} \) and \( \frac{5}{7} \), you multiply the numerators together and the denominators together:
\[ \frac{5}{3} \times \frac{5}{7} = \frac{5 \times 5}{3 \times 7} = \frac{25}{21} \]
So, \( \frac{5}{3} \times \frac{5}{7} = \frac{25}{21} \).