\( 19 \cdot \frac{5}{17} + 81 : \frac{2}{5} = \frac{95}{17} + 81 \cdot \frac{5}{2} = \frac{95}{17} + \frac{405}{2} = \frac{95 \cdot 2}{17 \cdot 2} + \frac{405 \cdot 17}{2 \cdot 17} = \frac{190}{34} + \frac{6885}{34} = \frac{7075}{34} \)
Ответ: \( \frac{7075}{34} \).