Выполним действия:
$$4\frac{2}{3}+1\frac{1}{3}-3-5\frac{1}{6} = \frac{14}{3} + \frac{4}{3} - 3 - \frac{31}{6} = \frac{18}{3} - 3 - \frac{31}{6} = 6 - 3 - \frac{31}{6} = 3 - \frac{31}{6} = \frac{18}{6} - \frac{31}{6} = -\frac{13}{6} = -2\frac{1}{6}$$Ответ: $$-2\frac{1}{6}$$