5) $$\frac{10}{11} : \frac{12}{2\frac{21}{22}} \cdot 6 \frac{1}{2} = \frac{10}{11} : \frac{12}{\frac{65}{22}} \cdot \frac{13}{2} = \frac{10}{11} \cdot \frac{22}{12} \cdot \frac{65}{1} \cdot \frac{13}{2} = \frac{10}{1} \cdot \frac{2}{12} \cdot \frac{65}{1} \cdot \frac{13}{2} = \frac{8450}{12} = 704 \frac{1}{6}$$
Ответ: $$704 \frac{1}{6}$$