5) \(\left(5\frac{1}{3}+1\frac{2}{3}\right)\cdot\frac{13}{14}+\left(2\frac{1}{9}-1\frac{1}{6}\right):\frac{17}{15}\)

Вычислим выражения в скобках:

\(5\frac{1}{3}+1\frac{2}{3}=7\).

\(7\cdot\frac{13}{14}=\frac{13}{2}\).

\(2\frac{1}{9}-1\frac{1}{6}=\frac{19}{9}-\frac{7}{6}=\frac{38-21}{18}=\frac{17}{18}\).

\(\frac{17}{18}:\frac{17}{15}=\frac{17}{18}\cdot\frac{15}{17}=\frac{5}{6}\).

\(\frac{13}{2}+\frac{5}{6}=\frac{39}{6}+\frac{5}{6}=\frac{44}{6}=\frac{22}{3}=7\frac{1}{3}\).

Ответ: \(7\frac{1}{3}\).