$\sqrt{3}-\sqrt{5}(\sqrt{10}-\sqrt{2}).(3+\sqrt{5})\\=\sqrt{3}+(-\sqrt{50}+\sqrt{10}).(3+\sqrt{5})\\=\sqrt{3}+(-5\sqrt{2}+\sqrt{10}).(3+\sqrt{5})\\=\sqrt{3}-15\sqrt{2}-5\sqrt{10}+3\sqrt{10}+\sqrt{50}\\=\sqrt{3}-15\sqrt{2}-5\sqrt{10}+3\sqrt{10}+5\sqrt{2}\\=\sqrt{3}-10\sqrt{2}-2\sqrt{10}$