{5 \choose 2}(\frac{1}{5})^2 \cdot {3 \choose 2}(\frac{2}{5})^2\cdot\frac{2}{5}=\frac{5!}{2!2!} \cdot \frac{2}{10}\cdot \frac{2}{10}\cdot \frac{4}{10}\cdot \frac{4}{10}\cdot \frac{4}{10}=\frac{240}{3125}=0.0768.