\(\dfrac{5}{13}+\dfrac{-5}{17}+\dfrac{-20}{41}+\dfrac{8}{13}+\dfrac{-21}{41}\)
\(=\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\dfrac{-5}{17}+\left(\dfrac{-20}{41}-\dfrac{21}{41}\right)\)
\(=\dfrac{13}{13}+\dfrac{-5}{17}+\dfrac{-41}{41}\)
\(=1-\dfrac{5}{17}-1\)
\(=-\dfrac{5}{17}\)