$\dfrac{-5}{9}+\dfrac{8}{15}+\dfrac{-2}{11}+\dfrac{4}{-9}+\dfrac{7}{15}$
$=\dfrac{-5}{9}+\dfrac{8}{15}+\dfrac{-2}{11}+\dfrac{-4}{9}+\dfrac{7}{15}$
$=(\dfrac{-5}{9}+\dfrac{-4}{9})+(\dfrac{8}{15}+\dfrac{7}{15})+\dfrac{-2}{11}$
$=\dfrac{-9}{9}+\dfrac{15}{15}+\dfrac{-2}{11}$
$=(-1)+1+\dfrac{-2}{11}$
$=0+\dfrac{-2}{11}$
$=\dfrac{-2}{11}$