\(\left(\frac{3}{4}\cdot\frac{2}{9}+\frac{5}{8}\right):\frac{2}{5}\)

\(\frac{3}{4}\cdot\frac{2}{9}=\frac{1}{6}\), поэтому \(\frac{1}{6}+\frac{5}{8}=\frac{19}{24}\).

\(\frac{19}{24}:\frac{2}{5}=\frac{19}{24}\cdot\frac{5}{2}=\frac{95}{48}=1\frac{47}{48}\).

Ответ: \(1\frac{47}{48}\).