$$\frac{5}{14} + (-3\frac{1}{3} + \frac{5}{11} \cdot 4\frac{2}{5}) : \frac{7}{12} = \frac{5}{14} + (-\frac{10}{3} + \frac{5}{11} \cdot \frac{22}{5}) : \frac{7}{12} =$$
$$\frac{5}{14} + (-\frac{10}{3} + \frac{5 \cdot 22}{11 \cdot 5}) : \frac{7}{12} = \frac{5}{14} + (-\frac{10}{3} + \frac{2}{1}) : \frac{7}{12} = \frac{5}{14} + (-\frac{10}{3} + 2) : \frac{7}{12} =$$
$$\frac{5}{14} + (-\frac{10}{3} + \frac{6}{3}) : \frac{7}{12} = \frac{5}{14} + (\frac{-10+6}{3}) : \frac{7}{12} = \frac{5}{14} + (\frac{-4}{3}) : \frac{7}{12} = \frac{5}{14} + (\frac{-4}{3} \cdot \frac{12}{7}) =$$
$$\frac{5}{14} + (\frac{-4 \cdot 12}{3 \cdot 7}) = \frac{5}{14} + (\frac{-4 \cdot 4}{1 \cdot 7}) = \frac{5}{14} + (\frac{-16}{7}) = \frac{5}{14} + (\frac{-32}{14}) = \frac{5-32}{14} = \frac{-27}{14} = -1\frac{13}{14}$$
Ответ: $$-1\frac{13}{14}$$