$\sqrt{7-2\sqrt{10}}-\sqrt{6+2\sqrt{5}}+\sqrt{2}+5=4_{}$
+)BĐVT:$=\sqrt{2-2\sqrt{10}-5}-\sqrt{1+2\sqrt{5}+5}+\sqrt{2}+5_{}$
$=\sqrt{(\sqrt{2}-\sqrt{5})^2}-\sqrt{(1+\sqrt{5})^2}+\sqrt{2}+5_{}$
$=\sqrt{(\sqrt{5}-\sqrt{2})^2}-\sqrt{(\sqrt{5}^2+1)}+\sqrt{2}+5_{}$
$|\sqrt[]{5} -\sqrt[]{2}|-|\sqrt[]{5}+1| +\sqrt[]{2}+5$
$=\sqrt{5}-\sqrt{2}-1-\sqrt{5}+\sqrt{2}+5_{}$
`=4`
+)Sau khi biến đổi, ta có:VT=VP(đpcm)