\[\left( \frac{m + 5^{\backslash m + 5}}{m - 5} - \frac{m^{\backslash m - 5}}{m + 5} \right) \cdot \frac{m + 5}{3m + 5} =\]
\[= \frac{m^{2} + 10m + 25 - m^{2} + 5m}{(m - 5)(m + 5)} \cdot \frac{m + 5}{3m + 5} =\]
\[= \frac{15m + 25}{(m - 5)(3m + 5)} =\]
\[= \frac{5 \cdot (3m + 5)}{(m - 5)(3m + 5)} = \frac{5}{m - 5}.\]