\(5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}\\ =5\sqrt{3}+5\sqrt{48-10\sqrt{\left(2+\sqrt{3}\right)^2}}\\ =5\sqrt{3}+5\sqrt{48-10\left|2+\sqrt{3}\right|}\\ =5\sqrt{3}+5\sqrt{48-10\left(2+\sqrt{3}\right)}\\ =5\sqrt{3}+5\sqrt{48-20-10\sqrt{3}}\\ =5\sqrt{3}+5\sqrt{28-10\sqrt{3}}\\ =5\sqrt{3}+5\sqrt{25-10\sqrt{3}+3}\\ =5\sqrt{3}+5\sqrt{\left(5-\sqrt{3}\right)^2}\\ =5\sqrt{3}+5\left|5-\sqrt{3}\right|\\ =5\sqrt{3}+5\left(5-\sqrt{3}\right)\\ =5\sqrt{3}+25-5\sqrt{3}=25\)
\(5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}\)
\(=5\sqrt{3}+5\sqrt{48-10\sqrt{\left(\sqrt{3}+2\right)^2}}\)
\(=5\sqrt{3}+5\sqrt{48-10\left(\sqrt{3}+2\right)}\)
\(=5\sqrt{3}+5\sqrt{48-10\sqrt{3}-20}\)
\(=5\sqrt{3}+5\sqrt{28-10\sqrt{3}}\)
\(=5\sqrt{3}+5\sqrt{\left(5-\sqrt{3}\right)^2}\)
\(=5\sqrt{3}+5\left(5-\sqrt{3}\right)\)
\(=5\sqrt{3}+25-5\sqrt{3}\)
= 25
