To solve the problem \(-\frac{5}{9} \div \frac{1}{5}\), we multiply by the reciprocal of the second fraction:
\[ -\frac{5}{9} \div \frac{1}{5} = -\frac{5}{9} \times \frac{5}{1} \]
Now, multiply the numerators and the denominators:
\[ -\frac{5 \times 5}{9 \times 1} = -\frac{25}{9} \]
Next, we want to convert \(-\frac{25}{9}\) into a mixed number. We do this by dividing \(25\) by \(9\):
\[ 25 \div 9 = 2 \quad \text{with a remainder of } 7 \]
This means:
\[ -\frac{25}{9} = -2 \frac{7}{9} \]
Thus, the final answer as a mixed number is:
\[ -2 \frac{7}{9} \]