Решение:

$$ \left(\frac{19}{8} + \frac{11}{12}\right) : \frac{5}{48} = \left(\frac{19 \cdot 3}{8 \cdot 3} + \frac{11 \cdot 2}{12 \cdot 2}\right) : \frac{5}{48} = \left(\frac{57}{24} + \frac{22}{24}\right) : \frac{5}{48} = \frac{57+22}{24} : \frac{5}{48} = \frac{79}{24} : \frac{5}{48} = \frac{79}{24} \cdot \frac{48}{5} = \frac{79 \cdot 48}{24 \cdot 5} = \frac{79 \cdot 2}{5} = \frac{158}{5} = 31\frac{3}{5} $$

Ответ: $$31\frac{3}{5}$$