To multiply the fractions \( \frac{8}{9} \) and \( \frac{5}{7} \), you multiply the numerators together and the denominators together:
\[ \frac{8}{9} \times \frac{5}{7} = \frac{8 \times 5}{9 \times 7} = \frac{40}{63} \]
So, \( \frac{8}{9} \times \frac{5}{7} = \frac{40}{63} \).