\(\frac{5}{13}+\left(-\frac{5}{7}\right)+\left(-\frac{20}{41}\right)+\frac{8}{13}+\left(-\frac{21}{41}\right)\)
\(=\left(\frac{5}{13}+\frac{8}{13}\right)+\left(-\frac{20}{41}+\frac{-21}{41}\right)+\left(-\frac{5}{7}\right)\)
\(=1+\left(-1\right)+\left(-\frac{5}{7}\right)\)
\(=0+\left(-\frac{5}{7}\right)=-\frac{5}{7}\)
\(\left(\frac{5}{13}+\frac{8}{13}\right)+\left(\frac{-20}{41}+\frac{-21}{41}\right)+\frac{-5}{7}\)
\(=1+\left(-1\right)+\frac{-5}{7}\)
\(=\left(1-1\right)+\frac{-5}{7}\)
\(=0+\frac{-5}{7}\)
\(=\frac{-5}{7}\)