\[\boxed{\text{5.\ 14}}\]
\[\textbf{а)} - 6\frac{2}{6} + 4\frac{5}{9} = - \left( 6\frac{1}{3} - 4\frac{5}{9} \right) =\]
\[= - \left( 6\frac{3}{9} - 4\frac{5}{9} \right) =\]
\[= - \left( 5\frac{12}{9} - 4\frac{5}{9} \right) = - 1\frac{7}{9}\]
\[\textbf{б)}\ 2\frac{4}{15} - 3\frac{11}{20} =\]
\[= - \left( 3\frac{33}{60} - 2\frac{16}{60} \right) = - 1\frac{17}{60}\]
\[\textbf{в)} - 2\frac{2}{15} - 4\frac{7}{10} =\]
\[= - 2\frac{4}{30} - 4\frac{21}{30} = - 6\frac{25}{30} = - 6\frac{5}{6}\]
\[\textbf{г)} - 8\frac{5}{6} + \frac{7}{10} = - \left( 8\frac{25}{30} - \frac{21}{30} \right) =\]
\[= - 8\frac{4}{30} = - 8\frac{2}{15}\]