\(\sqrt{13-4\sqrt{10}}-\sqrt{53+12\sqrt{10}}=\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}-\sqrt{\left(3\sqrt{5}-2\sqrt{2}\right)^2}\)
\(=\left|2\sqrt{2}-\sqrt{5}\right|-\left|3\sqrt{5}-2\sqrt{2}\right|=2\sqrt{2}-\sqrt{5}-\left(3\sqrt{5}-2\sqrt{2}\right)\)
\(=4\sqrt{2}-4\sqrt{5}\)







