Вычислить: \(0,2+\dfrac{(5\frac{1}{25}\cdot7,125+5,04):9,2\cdot\frac{8}{27}}{2-1\frac{2}{3}:1,5}\cdot\frac{8}{15}\).

1. \(5\frac{1}{25}\cdot7,125+5,04=\frac{126}{25}\cdot\frac{57}{8}+\frac{126}{25}=\frac{4599}{200}\).
2. Числитель дроби:
   \(\frac{4599}{200}:9,2\cdot\frac{8}{27}=\frac{4599}{200}:\frac{46}{5}\cdot\frac{8}{27}=\frac{511}{690}\).
3. Знаменатель дроби:
   \(2-1\frac{2}{3}:1,5=2-\frac{5}{3}:\frac{3}{2}=2-\frac{10}{9}=\frac{8}{9}\).
4. \(\frac{511}{690}:\frac{8}{9}=\frac{1533}{1840}\).
5. \(0,2+\frac{1533}{1840}\cdot\frac{8}{15}=\frac{1}{5}+\frac{511}{1150}=\frac{741}{1150}\).

Ответ: \(\frac{741}{1150}\).