#### Answer

$\sqrt{22}+\sqrt{55}-\sqrt{14}-\sqrt{35}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
(\sqrt{11}-\sqrt{7})(\sqrt{2}+\sqrt{5})
,$ use FOIL and the properties of radicals.
$\bf{\text{Solution Details:}}$
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\sqrt{11}(\sqrt{2})+\sqrt{11}(\sqrt{5})-\sqrt{7}(\sqrt{2})-\sqrt{7}(\sqrt{5})
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\sqrt{11(2)}+\sqrt{11(5)}-\sqrt{7(2)}-\sqrt{7(5)}
\\\\=
\sqrt{22}+\sqrt{55}-\sqrt{14}-\sqrt{35}
.\end{array}