$$\frac{6}{5} + \frac{12}{35} \cdot \frac{13}{15} + 5 \cdot \frac{2}{7} = \frac{6}{5} + \frac{4 \cdot 13}{35 \cdot 5} + \frac{10}{7} = \frac{6}{5} + \frac{52}{175} + \frac{10}{7} = \frac{6 \cdot 35 + 52 + 10 \cdot 25}{175} = \frac{210 + 52 + 250}{175} = \frac{512}{175}$$