5) \(\dfrac{-2\frac{2}{11}\cdot4,125+1,6\cdot9\frac34}{9-5\frac56\cdot2\frac47}\)

Преобразуем числа: \(-2\frac{2}{11}=-\frac{24}{11}\), \(4,125=\frac{33}{8}\), \(1,6=\frac85\), \(9\frac34=\frac{39}{4}\), \(5\frac56=\frac{35}{6}\), \(2\frac47=\frac{18}{7}\).

Числитель:

\[-\frac{24}{11}\cdot\frac{33}{8}+\frac85\cdot\frac{39}{4}=-9+\frac{78}{5}=\frac{33}{5}.\]

Знаменатель:

\[9-\frac{35}{6}\cdot\frac{18}{7}=9-15=-6.\]

\[\frac{33}{5}:(-6)=-\frac{11}{10}.\]

Ответ: \(-\frac{11}{10}=-1,1\).