\(\left(10\sqrt{\dfrac{3}{5}}-\dfrac{3\sqrt{5}-5\sqrt{3}}{\sqrt{3}-\sqrt{5}}+4\right)\cdot\sqrt{\left(\sqrt{15}-4\right)^2}\)
\(=\left[\dfrac{10\sqrt{3}}{\sqrt{5}}-\dfrac{\sqrt{15}\left(\sqrt{3}-\sqrt{5}\right)}{\sqrt{3}-\sqrt{5}}+4\right]\cdot\left|\sqrt{15}-4\right|\)
\(=\left(\dfrac{2\sqrt{5}\cdot\sqrt{3}\cdot\sqrt{5}}{\sqrt{5}}-\sqrt{15}+4\right)\cdot\left(4-\sqrt{15}\right)\)
\(=\left(2\sqrt{5}\cdot\sqrt{3}-\sqrt{15}+4\right)\cdot\left(4-\sqrt{15}\right)\)
\(=\left(4+2\sqrt{15}-\sqrt{15}\right)\cdot\left(4-\sqrt{15}\right)\)
\(=\left(4+\sqrt{15}\right)\cdot\left(4-\sqrt{15}\right)\)
\(=4^2-\left(\sqrt{15}\right)^2\)
\(=16-15\)
\(=1\)
