5) \(\left(5\frac{1}{3}+1\frac{2}{3}\right)\cdot\frac{3}{14}+\left(2\frac{1}{9}-1\frac{1}{6}\right):\frac{4}{15}\); 6) \(\frac{8}{25}\cdot\frac{45}{12}:\left(1\frac{1}{14}-1\frac{1}{21}\right)\cdot\frac{5}{27}+5\frac{2}{3}\)

5) \(5\frac{1}{3}+1\frac{2}{3}=7\), поэтому \(7\cdot\frac{3}{14}=\frac{3}{2}\).

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

\(\frac{17}{18}:\frac{4}{15}=\frac{17}{18}\cdot\frac{15}{4}=\frac{85}{24}\).

\(\frac{3}{2}+\frac{85}{24}=\frac{36}{24}+\frac{85}{24}=\frac{121}{24}=5\frac{1}{24}\).

Ответ: \(5\frac{1}{24}\).

6) \(\frac{8}{25}\cdot\frac{45}{12}=\frac{6}{5}\).

\(1\frac{1}{14}-1\frac{1}{21}=\frac{1}{14}-\frac{1}{21}=\frac{1}{42}\), поэтому \(\frac{6}{5}:\frac{1}{42}=\frac{252}{5}\).

\(\frac{252}{5}\cdot\frac{5}{27}=\frac{28}{3}\).

\(\frac{28}{3}+5\frac{2}{3}=\frac{28}{3}+\frac{17}{3}=15\).

Ответ: \(15\).