4) $$\left(-1\frac{3}{8}-2\frac{5}{12}\right): 5\frac{5}{12}.$$

Решим пример по действиям:

1. $$-1\frac{3}{8} - 2\frac{5}{12} = -\frac{1 \cdot 8 + 3}{8} - \frac{2 \cdot 12 + 5}{12} = -\frac{11}{8} - \frac{29}{12} = -\frac{11 \cdot 3}{8 \cdot 3} - \frac{29 \cdot 2}{12 \cdot 2} = -\frac{33}{24} - \frac{58}{24} = -\frac{33 + 58}{24} = -\frac{91}{24};$$
2. $$5\frac{5}{12} = \frac{5 \cdot 12 + 5}{12} = \frac{60 + 5}{12} = \frac{65}{12};$$
3. $$-\frac{91}{24} : \frac{65}{12} = -\frac{91}{24} \cdot \frac{12}{65} = -\frac{91 \cdot 12}{24 \cdot 65} = -\frac{91}{2 \cdot 65} = -\frac{91}{130}.$$

Ответ: $$-\frac{91}{130}$$.