\[\frac{a - 5}{5a^{3}} - \frac{1 - a}{a^{4}} =\]
\[= \frac{a(a - 5) - 5(1 - a)}{5a^{4}} =\]
\[= \frac{a^{2} - 5a - 5 + 5a}{5a^{4}} = \frac{a^{2} - 5}{5a^{4}}.\]