2) $$\left(5\frac{8}{9} : 1\frac{17}{36}+1\frac{1}{4}\right) \cdot \frac{5}{21};$$

Решим пример по действиям:

1. $$5\frac{8}{9} : 1\frac{17}{36} = \frac{5 \cdot 9 + 8}{9} : \frac{1 \cdot 36 + 17}{36} = \frac{53}{9} : \frac{53}{36} = \frac{53}{9} \cdot \frac{36}{53} = \frac{53 \cdot 36}{9 \cdot 53} = \frac{36}{9} = 4;$$
2. $$1\frac{1}{4} = \frac{1 \cdot 4 + 1}{4} = \frac{5}{4};$$
3. $$4 + \frac{5}{4} = \frac{4 \cdot 4 + 5}{4} = \frac{16 + 5}{4} = \frac{21}{4};$$
4. $$\frac{21}{4} \cdot \frac{5}{21} = \frac{21 \cdot 5}{4 \cdot 21} = \frac{5}{4} = 1\frac{1}{4}.$$

Ответ: $$1\frac{1}{4}$$.