\(\dfrac{5}{9}\cdot\dfrac{7}{13}+\dfrac{5}{9}\cdot\dfrac{9}{13}-\dfrac{5}{9}:\dfrac{13}{3}\\ =\dfrac{5}{9}\cdot\dfrac{7}{13}+\dfrac{5}{9}\cdot\dfrac{9}{13}-\dfrac{5}{9}\cdot\dfrac{3}{13}\\ =\dfrac{5}{9}\cdot\left(\dfrac{7}{13}+\dfrac{9}{13}-\dfrac{3}{13}\right)\\ =\dfrac{5}{9}\cdot1=\dfrac{5}{9}\)
\(\dfrac{5}{9}\cdot\dfrac{7}{13}+\dfrac{5}{9}\cdot\dfrac{9}{13}-\dfrac{5}{9}:\dfrac{13}{3}\)
\(=\dfrac{5}{9}\cdot\dfrac{7}{13}+\dfrac{5}{9}\cdot\dfrac{9}{13}-\dfrac{5}{9}\cdot\dfrac{3}{13}\)
\(=\dfrac{5}{9}\cdot\left(\dfrac{7}{13}+\dfrac{9}{13}-\dfrac{3}{13}\right)\)
\(=\dfrac{5}{9}\cdot\left(\dfrac{7+9-3}{13}\right)\)
\(=\dfrac{5}{9}\cdot\dfrac{13}{13}\)
\(=\dfrac{5}{9}\cdot1=\dfrac{5}{9}\)