5. \(2\frac{2}{5}\cdot\frac{5}{6}-\frac{3}{4}\cdot1\frac{2}{3}\)

Преобразуем смешанные числа: \(2\frac{2}{5}=\frac{12}{5}\), \(1\frac{2}{3}=\frac{5}{3}\).

\(\frac{12}{5}\cdot\frac{5}{6}=2\), \(\frac{3}{4}\cdot\frac{5}{3}=\frac{5}{4}\).

\(2-\frac{5}{4}=\frac{8}{4}-\frac{5}{4}=\frac{3}{4}\).

Ответ: \(\frac{3}{4}\).