To divide fractions, you multiply by the reciprocal of the second fraction.
So, \( \frac{1}{7} \div \frac{1}{5} \) can be rewritten as:
\[ \frac{1}{7} \times \frac{5}{1} \]
Now, multiply the numerators and the denominators:
\[ \frac{1 \times 5}{7 \times 1} = \frac{5}{7} \]
Thus, \( \frac{1}{7} \div \frac{1}{5} = \frac{5}{7} \).