To multiply the fractions \( \frac{5}{7} \times \frac{4}{9} \), you multiply the numerators together and the denominators together:
\[ \text{Numerator: } 5 \times 4 = 20 \] \[ \text{Denominator: } 7 \times 9 = 63 \]
Thus, the product of the fractions is:
\[ \frac{20}{63} \]
So the correct answer is \( \frac{20}{63} \).