Answer
$-8\sqrt{5}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, the expression $
(\sqrt{5}-5)(2\sqrt{5}+2)
$ simplifies to
\begin{array}{l}
(\sqrt{5})(2\sqrt{5})+(\sqrt{5})(2)-5(2\sqrt{5})-5(2)
\\=
2\sqrt{25}+2\sqrt{5}-10\sqrt{5}-10
\\=
2\cdot5-8\sqrt{5}-10
\\=
10-8\sqrt{5}-10
\\=
-8\sqrt{5}
.\end{array}
