5) \(=\dfrac{5\left(\sqrt{21}+4\right)}{21-16}+\dfrac{-\sqrt{21}\left(\sqrt{7}-\sqrt{3}\right)}{\sqrt{7}-\sqrt{3}}\)
\(=\sqrt{21}+4-\sqrt{21}=4\)
6) \(=\dfrac{8\left(3-\sqrt{5}\right)}{9-5}-\dfrac{\sqrt{5}\left(\sqrt{3}-2\right)}{\sqrt{3}-2}\)
\(=6-2\sqrt{5}-\sqrt{5}=6-3\sqrt{5}\)
\(5.\dfrac{5}{\sqrt{21}-4}+\dfrac{3\sqrt{7}-7\sqrt{3}}{\sqrt{7}-\sqrt{3}}\\ =\dfrac{5\left(\sqrt{21}+4\right)}{21-16}+\dfrac{\sqrt{3}.\sqrt{7}\left(\sqrt{7}-\sqrt{3}\right)}{\sqrt{7}-\sqrt{3}}\\ =\dfrac{5\left(\sqrt{21}+4\right)}{5}+\sqrt{21}\\ =\sqrt{21}+4+\sqrt{21}=4+2\sqrt{21}\)
\(6.\dfrac{8}{3+\sqrt{5}}-\dfrac{\sqrt{15}-2\sqrt{5}}{\sqrt{3}-2}\\ =\dfrac{8\left(3-\sqrt{5}\right)}{9-5}-\dfrac{\left(\sqrt{15}-2\sqrt{5}\right)\left(\sqrt{3}+2\right)}{3-4}\\ =2\left(3-\sqrt{5}\right)+\sqrt{15}.\sqrt{3}+2\sqrt{15}-2\sqrt{15}-4\sqrt{5}\\ =6-2\sqrt{5}+3\sqrt{5}+2\sqrt{15}-2\sqrt{15}-4\sqrt{5}\\ =6-3\sqrt{5}\)