To find the quotient of \( \frac{7}{8} \div 5 \), you can rewrite the division by 5 as multiplication by the reciprocal of 5, which is \( \frac{1}{5} \):
\[ \frac{7}{8} \div 5 = \frac{7}{8} \times \frac{1}{5} \]
Now multiply the fractions:
\[ \frac{7 \times 1}{8 \times 5} = \frac{7}{40} \]
The fraction \( \frac{7}{40} \) is already in its simplest form. Thus, the final answer is:
\[ \frac{7}{40} \]