\[\boxed{\text{5.355.}}\]
\[1)\ \frac{5}{13} + \frac{4}{13} + \frac{6}{13} = \frac{5 + 4 + 6}{13} =\]
\[= \frac{15}{13} = 1\frac{2}{13}\ \]
\[\frac{5}{13} + \frac{4}{13} - \frac{6}{13} = \frac{5 + 4 - 6}{13} = \frac{3}{13}\ \]
\[2)\ \frac{9}{25} + \frac{6}{25} + \frac{2}{25} = \frac{9 + 6 + 2}{25} =\]
\[= \frac{17}{25}\ \]
\[\frac{9}{25} - \frac{6}{25} + \frac{2}{25} = \frac{9 - 6 + 2}{25} =\]
\[= \frac{5}{25} = \frac{1}{5}\ \]
\[3)\ 5\frac{2}{7} + 4\frac{1}{7} + 3\frac{4}{7} = 9\frac{3}{7} + 3\frac{4}{7} =\]
\[= 12\frac{7}{7} = 13\ \]
\[5\frac{2}{7} - 4\frac{1}{7} + 3\frac{4}{7} = 1\frac{1}{7} + 3\frac{4}{7} = 4\frac{5}{7}\ \]
\[4)\ 9\frac{5}{14} + 1\frac{3}{14} + 6\frac{1}{14} =\]
\[= 10\frac{8}{14} + 6\frac{1}{14} = 16\frac{9}{14}\ \]
\[9\frac{5}{14} + 1\frac{3}{14} - 6\frac{1}{14} =\]
\[= 10\frac{8}{14} - 6\frac{1}{14} = 4\frac{7}{14} = 4\frac{1}{2}\text{\ \ }\]