\[- \frac{3^{\backslash 7}}{11} - \frac{5^{\backslash 11}}{7} = - \frac{21}{77} - \frac{55}{77} =\]
\[= - \frac{76}{77} < 0\]
\[\frac{5}{7} - \frac{3}{7} = \frac{2}{7} > 0\]
\[- \frac{76}{77} < \frac{2}{7} \Longrightarrow - \frac{3}{11} - \frac{5}{7} < \frac{5}{7} - \frac{3}{7}.\]