\[m + n = 8;\ \ \ \ p = 3:\]
\[\frac{5}{m + n} - \frac{2}{p} = \frac{5}{8} - \frac{2}{3} =\]
\[= \frac{5 \cdot 3 - 2 \cdot 8}{24} = - \frac{1}{24}.\]