Решение:
$$5\frac{1}{9} - 2\frac{4}{9} = \frac{5 \cdot 9 + 1}{9} - \frac{2 \cdot 9 + 4}{9} = \frac{46}{9} - \frac{22}{9} = \frac{46 - 22}{9} = \frac{24}{9} = 2\frac{6}{9} = 2\frac{2}{3}$$
Ответ: $$2\frac{2}{3}$$