д) \(\left(5\frac{8}{15}-4\frac{7}{10}\right)\cdot2\frac{2}{3}-\frac{5}{9}\);

Преобразуем смешанные числа:

\(5\frac{8}{15}=\frac{83}{15}\), \(4\frac{7}{10}=\frac{47}{10}\), \(2\frac{2}{3}=\frac{8}{3}\).

\[\left(\frac{83}{15}-\frac{47}{10}\right)\cdot\frac{8}{3}-\frac{5}{9}=\left(\frac{166}{30}-\frac{141}{30}\right)\cdot\frac{8}{3}-\frac{5}{9}=\frac{5}{6}\cdot\frac{8}{3}-\frac{5}{9}.\]

\[\frac{5}{6}\cdot\frac{8}{3}-\frac{5}{9}=\frac{20}{9}-\frac{5}{9}=\frac{15}{9}=\frac{5}{3}.\]

Ответ: \(\frac{5}{3}\).