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$...=\sqrt{7}-\sqrt{2}-\frac{5}{\sqrt{7+2\sqrt{14}+2}}=\sqrt{7}-\sqrt{2}-\frac{5}{\sqrt{(\sqrt{7})^2+2*\sqrt{7}*\sqrt{2}+(\sqrt{2})^2}}=\\=\sqrt{7}-\sqrt{2}-\frac{5}{\sqrt{(\sqrt{7}+\sqrt{2})^2}}=\sqrt{7}-\sqrt{2}-\frac{5}{|\sqrt{7}+\sqrt{2}|}=\\=\sqrt{7}-\sqrt{2}-\frac{5}{\sqrt{7}+\sqrt{2}}=\sqrt{7}-\sqrt{2}-\frac{5*(\sqrt{7}-\sqrt{2})}{(\sqrt{7}+\sqrt{2})*(\sqrt{7}-\sqrt{2})}=\\=\sqrt{7}-\sqrt{2}-\frac{5(\sqrt{7}-\sqrt{2})}{(\sqrt{7})^2-(\sqrt{2})^2}=\sqrt{7}-\sqrt{2}-\frac{5(\sqrt{7}-\sqrt{2})}{5}=$
$=\sqrt{7}-\sqrt{2}-(\sqrt{7}-\sqrt{2})=\sqrt{7}-\sqrt{2}-\sqrt{7}+\sqrt{2}=0$