To find the quotient of \( \frac{7}{8} \div 5 \), you can rewrite the division of a fraction by a whole number as follows:
\[ \frac{7}{8} \div 5 = \frac{7}{8} \times \frac{1}{5} \]
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, as 7 and 40 have no common factors other than 1.
Thus, the answer is:
\[ \frac{7}{40} \]