To divide fractions, you multiply the first fraction by the reciprocal of the second fraction.
So, to divide \( \frac{4}{7} \) by \( \frac{4}{5} \):
\[ \frac{4}{7} \div \frac{4}{5} = \frac{4}{7} \times \frac{5}{4} \]
Now, multiply the numerators and the denominators:
\[ \frac{4 \times 5}{7 \times 4} = \frac{20}{28} \]
Now, simplify \( \frac{20}{28} \):
\[ \frac{20 \div 4}{28 \div 4} = \frac{5}{7} \]
So, the answer is \( \frac{5}{7} \).