To divide \( \frac{8}{9} \) by \( 5 \), you can rewrite the division as multiplication by the reciprocal:
\[ \frac{8}{9} \div 5 = \frac{8}{9} \times \frac{1}{5} \]
Now, multiply the fractions:
\[ \frac{8 \times 1}{9 \times 5} = \frac{8}{45} \]
So, the quotient of \( \frac{8}{9} \div 5 \) is \( \frac{8}{45} \). This fraction cannot be simplified further, so the final answer is:
\[ \frac{8}{45} \]