To divide fractions, you multiply by the reciprocal of the divisor.
So, to divide \( \frac{5}{6} \) by \( \frac{5}{7} \), you multiply \( \frac{5}{6} \) by the reciprocal of \( \frac{5}{7} \):
\[ \frac{5}{6} \div \frac{5}{7} = \frac{5}{6} \times \frac{7}{5} \]
Now, multiplying the numerators and the denominators:
\[ \frac{5 \times 7}{6 \times 5} = \frac{35}{30} \]
Next, simplify \( \frac{35}{30} \):
Both the numerator and the denominator can be divided by 5:
\[ \frac{35 \div 5}{30 \div 5} = \frac{7}{6} \]
So, \( \frac{5}{6} \div \frac{5}{7} = \frac{7}{6} \).