To find the quotient of \(-\frac{5}{9} \div \frac{1}{5}\), we can rewrite the division of fractions as multiplication by the reciprocal of the second fraction:
\[ -\frac{5}{9} \div \frac{1}{5} = -\frac{5}{9} \times \frac{5}{1} \]
Now, we can multiply the fractions:
\[ -\frac{5 \times 5}{9 \times 1} = -\frac{25}{9} \]
Next, we want to express \(-\frac{25}{9}\) as a mixed number. We first divide \(25\) by \(9\):
\[ 25 \div 9 = 2 \quad \text{(since } 9 \times 2 = 18\text{)} \]
The remainder is:
\[ 25 - 18 = 7 \]
Thus, \(-\frac{25}{9}\) can be expressed as:
\[ -2 \frac{7}{9} \]
Putting it all together, the final answer is:
\[ -2 \frac{7}{9} \]