To find the quotient of \(-\frac{5}{9} \div \frac{1}{5}\), we can multiply by the reciprocal of the second fraction:
\[ -\frac{5}{9} \div \frac{1}{5} = -\frac{5}{9} \times \frac{5}{1} \]
Now we multiply the fractions:
\[ -\frac{5 \times 5}{9 \times 1} = -\frac{25}{9} \]
Next, we convert \(-\frac{25}{9}\) into a mixed number. To do this, we divide the numerator by the denominator:
\[ 25 \div 9 = 2 \quad \text{(with a remainder of 7)} \]
So we can write:
\[ -\frac{25}{9} = -2 \frac{7}{9} \]
Thus, the answer as a mixed number is:
\[ \boxed{-2 \frac{7}{9}} \]