\( \left( 35 \frac{5}{6} : \frac{7}{18} - 5 \frac{3}{4} : 8 \frac{3}{12} \right) \cdot \frac{5}{15} \)

Решение:

Выполним действия по порядку:

1. \( 35 \frac{5}{6} = \frac{215}{6} \)
2. \( \frac{215}{6} : \frac{7}{18} = \frac{215}{6} \cdot \frac{18}{7} = \frac{215 \cdot 3}{7} = \frac{645}{7} \)
3. \( 5 \frac{3}{4} = \frac{23}{4} \)
4. \( 8 \frac{3}{12} = 8 \frac{1}{4} = \frac{33}{4} \)
5. \( \frac{23}{4} : \frac{33}{4} = \frac{23}{4} \cdot \frac{4}{33} = \frac{23}{33} \)
6. \( \frac{645}{7} - \frac{23}{33} = \frac{645 \cdot 33 - 23 \cdot 7}{231} = \frac{21285 - 161}{231} = \frac{21124}{231} \)
7. \( \frac{5}{15} = \frac{1}{3} \)
8. \( \frac{21124}{231} \cdot \frac{1}{3} = \frac{21124}{693} \)

Ответ: \( \frac{21124}{693} \).