√5 * (√(√2 - √5)² + √2)

[latex] \sqrt{5}\cdot \Big ( \sqrt{(\sqrt2-\sqrt5)^2}+\sqrt{2} \Big )=\sqrt5\cdot \Big (|\sqrt2-\sqrt5|+\sqrt2\Big )=\\\\=\sqrt5\cdot \Big ((\sqrt5-\sqrt2)+\sqrt2\Big )=\sqrt5\cdot \sqrt5=5\\\\\\Tak\; kak\; \; (\sqrt2-\sqrt5)\ \textless \ 0\; ,\; to\; \; |\sqrt2-\sqrt5|=-(\sqrt2-\sqrt5)=\sqrt5-\sqrt2[/latex]

√5 * (√(√2 - √5)² + √2)= √5*(√5 - √2 + √2) = √5*√5 = 5