7. \(\left(\frac{7}{8}-\frac{17}{12}\right):\frac{5}{12}\)

Приведём дроби к общему знаменателю: \(\frac{7}{8}=\frac{21}{24}\), \(\frac{17}{12}=\frac{34}{24}\).

\(\left(\frac{7}{8}-\frac{17}{12}\right):\frac{5}{12}=\left(\frac{21}{24}-\frac{34}{24}\right):\frac{5}{12}=\left(-\frac{13}{24}\right)\cdot\frac{12}{5}=-\frac{13}{10}\).

Ответ: \(-\frac{13}{10}\).