5) 1/2 + 1/3; 6) 12 3/8 − 8 1/6; 7) 24/65 · 39/40; 8) 1 3/5 : 5 1/3.

1. \(\frac{1}{2}+\frac{1}{3}=\frac{3}{6}+\frac{2}{6}=\frac{5}{6}\).
2. \(12\frac{3}{8}-8\frac{1}{6}=\frac{99}{8}-\frac{49}{6}=\frac{297-196}{24}=\frac{101}{24}=4\frac{5}{24}\).
3. \(\frac{24}{65}\cdot\frac{39}{40}=\frac{3}{65}\cdot\frac{39}{5}=\frac{117}{325}\).
4. Преобразуем смешанные числа: \(1\frac{3}{5}=\frac{8}{5}\), \(5\frac{1}{3}=\frac{16}{3}\). Тогда \(\frac{8}{5}:\frac{16}{3}=\frac{8}{5}\cdot\frac{3}{16}=\frac{3}{10}\).

Ответ: 5) \(\frac{5}{6}\); 6) \(4\frac{5}{24}\); 7) \(\frac{117}{325}\); 8) \(\frac{3}{10}\).