\(\dfrac{15}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}=\dfrac{3.5}{\sqrt{10}+2\sqrt{10}+2\sqrt{5}-\sqrt{5}-4\sqrt{5}}\)

\(=\dfrac{3.\left(10-5\right)}{3\sqrt{10}-3\sqrt{5}}=\dfrac{\left(\sqrt{10}-\sqrt{5}\right)\left(\sqrt{10}+\sqrt{5}\right)}{\sqrt{10}-\sqrt{5}}=\sqrt{10}+\sqrt{5}\)