\(\dfrac{5}{9}:(\dfrac{1}{11}-\dfrac{5}{22})+\dfrac{5}{9}:(\dfrac{1}{15}-\dfrac{2}{3})\)
\(=\dfrac{5}{9}:(\dfrac{2}{22}+\dfrac{-5}{22})+\dfrac{5}{9}:(\dfrac{1}{15}+\dfrac{-10}{15})\)
\(=\dfrac{5}{9}:\dfrac{-3}{22}+\dfrac{5}{9}:\dfrac{-9}{15}\)
\(=\dfrac{5}{9}\times\dfrac{-22}{3}+\dfrac{5}{9}\times\dfrac{-15}{9}\)
=\(\dfrac{5}{9}\times\left(-\dfrac{22}{3}+\dfrac{-15}{9}\right)\)
\(=\dfrac{5}{9}\times\left(-9\right)\)
\(=\left(-5\right)\)
\(\dfrac{5}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)+\dfrac{5}{9}:\left(\dfrac{1}{15}-\dfrac{2}{3}\right)=\dfrac{5}{9}:\left(\dfrac{-3}{22}\right)+\dfrac{5}{9}:\left(\dfrac{-3}{5}\right)\)
\(=\dfrac{5}{9}.\dfrac{22}{-3}+\dfrac{5}{9}.\dfrac{5}{-3}=\dfrac{5}{9}\left(\dfrac{22}{-3}+\dfrac{5}{-3}\right)=\dfrac{5}{9}.\dfrac{22+5}{-3}=\dfrac{5}{9}.\dfrac{27}{-3}\)
\(=\dfrac{5.27}{9.-3}=\dfrac{5.27}{-27}=-5\)