\(\left(\frac{10}{13} + \frac{15}{4}\right) \cdot \frac{26}{5} = \left(\frac{10 \cdot 4}{13 \cdot 4} + \frac{15 \cdot 13}{4 \cdot 13}\right) \cdot \frac{26}{5} = \left(\frac{40}{52} + \frac{195}{52}\right) \cdot \frac{26}{5} = \frac{235}{52} \cdot \frac{26}{5} = \frac{235 \cdot 26}{52 \cdot 5} = \frac{235 \cdot 1}{2 \cdot 5} = \frac{235}{10} = \frac{47}{2}\)
Ответ: \(\frac{47}{2}\)