\[\frac{1}{5 - c} + \frac{5}{c^{2} - 5c} =\]
\[= \frac{1^{\backslash c}}{5 - c} - \frac{5}{c(5 - c)} =\]
\[= \frac{c - 5}{c(5 - c)} = - \frac{1}{c}.\]