\(\left(5+\sqrt{21}\right)\left(\sqrt{14}-\sqrt{6}\right)\sqrt{5-\sqrt{21}}=\left(5+\sqrt{21}\right)\left(\sqrt{7}-\sqrt{3}\right)\sqrt{7-2\sqrt{7}.\sqrt{3}+3}=\left(5+\sqrt{21}\right)\left(\sqrt{7}-\sqrt{3}\right)^2=\left(5+\sqrt{21}\right)\left(10-2\sqrt{21}\right)=2\left(5+\sqrt{21}\right)\left(5-\sqrt{21}\right)=2\left(25-21\right)=2.4=8\)