Решение:
$$5\frac{4}{9} - 3 = \frac{5 \cdot 9 + 4}{9} - \frac{3 \cdot 9}{9} = \frac{49}{9} - \frac{27}{9} = \frac{49 - 27}{9} = \frac{22}{9} = 2\frac{4}{9}$$
Ответ: $$2\frac{4}{9}$$