Ответ:

\(1\frac{5}{12}=\frac{17}{12}\).

\(-\frac{5}{6}+\frac{2}{3}=-\frac{5}{6}+\frac{4}{6}=-\frac{1}{6}\).

\(\frac{17}{12}:\left(-\frac{1}{6}\right)=\frac{17}{12}\cdot(-6)=-\frac{17}{2}\).

Ответ: \(-\frac{17}{2}\).