$$ \frac{7}{9} \cdot 5\frac{2}{5} = \frac{7}{9} \cdot \frac{5 \cdot 5 + 2}{5} = \frac{7}{9} \cdot \frac{27}{5} = \frac{7 \cdot 27}{9 \cdot 5} = \frac{7 \cdot 3}{1 \cdot 5} = \frac{21}{5} = 4\frac{1}{5}$$.
Ответ: $$4\frac{1}{5}$$