To find the quotient of \( \frac{8}{9} \div 5 \), we can rewrite the division as a multiplication by the reciprocal.
So, we have:
\[ \frac{8}{9} \div 5 = \frac{8}{9} \times \frac{1}{5} \]
Now, we multiply the fractions:
\[ \frac{8 \times 1}{9 \times 5} = \frac{8}{45} \]
The fraction \( \frac{8}{45} \) is already in its simplest form, as 8 and 45 have no common factors other than 1.
Therefore, the final answer is:
\[ \frac{8}{45} \]