To find the quotient of \(-\frac{5}{9} \div \frac{1}{5}\), you can multiply by the reciprocal of \(\frac{1}{5}\):
\[ -\frac{5}{9} \div \frac{1}{5} = -\frac{5}{9} \times \frac{5}{1} = -\frac{5 \times 5}{9 \times 1} = -\frac{25}{9} \]
Now, to convert \(-\frac{25}{9}\) to a mixed number, divide \(25\) by \(9\):
- \(25 \div 9 = 2\) (since \(9 \times 2 = 18\) and \(9 \times 3 = 27\) which exceeds 25).
- The remainder is \(25 - 18 = 7\).
Thus, \(-\frac{25}{9}\) can be written as the mixed number:
\[ -2 \frac{7}{9} \]
Therefore, the answer is:
\[ -2 \frac{7}{9} \]