\[2\frac{1}{6} + \frac{5}{12}\ :\frac{5}{8} = 2\frac{1}{6} + \frac{5}{12} \cdot \frac{8}{5} =\]
\[= 2\frac{1}{6} + \frac{4}{6} = 2\frac{5}{6}.\]