\[\left| - 5\frac{1}{6} \right| - \left| - 1\frac{5}{12} \right| = 5\frac{1^{\backslash 2}}{6} - 1\frac{5}{12} =\]
\[= 5\frac{2}{12} - 1\frac{5}{12} = 4\frac{14}{12} - 1\frac{5}{12} =\]
\[= 3\frac{14 - 5}{12} = 3\frac{9}{12} = 3\frac{3}{4}\]