$$5\frac{9}{5} \cdot \frac{2}{3} = \frac{34}{5} \cdot \frac{2}{3} = \frac{34 \cdot 2}{5 \cdot 3} = \frac{68}{15} = 4\frac{8}{15}$$
$$\mathbf{Ответ: 4\frac{8}{15}}$$