5. Найдите значение выражения: $$\frac{29}{4}:5\frac{4}{5}-4\frac{3}{4}\cdot(3-1\frac{19}{30})$$

Выполним действия по порядку.

1) $$5\frac{4}{5}=\frac{5\cdot5+4}{5}=\frac{29}{5}$$

2) $$\frac{29}{4}:\frac{29}{5}=\frac{29}{4}\cdot\frac{5}{29}=\frac{29\cdot5}{4\cdot29}=\frac{5}{4}$$

3) $$4\frac{3}{4}=\frac{4\cdot4+3}{4}=\frac{19}{4}$$

4) $$1\frac{19}{30}=\frac{1\cdot30+19}{30}=\frac{49}{30}$$

5) $$3-\frac{49}{30}=\frac{3}{1}-\frac{49}{30}=\frac{3\cdot30}{1\cdot30}-\frac{49}{30}=\frac{90}{30}-\frac{49}{30}=\frac{41}{30}$$

6) $$\frac{19}{4}\cdot\frac{41}{30}=\frac{19\cdot41}{4\cdot30}=\frac{779}{120}$$

7) $$\frac{5}{4}-\frac{779}{120}=\frac{5\cdot30}{4\cdot30}-\frac{779}{120}=\frac{150}{120}-\frac{779}{120}=-\frac{629}{120}=-5\frac{29}{120}$$

Ответ: $$-5\frac{29}{120}$$