#### Answer

$-9-2\sqrt[]{6}$

#### Work Step by Step

Using the FOIL method and the properties of radicals, the given expression, $
(\sqrt[]{6}-5)(\sqrt[]{6}+3)
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[]{6}(\sqrt[]{6})+\sqrt[]{6}(3)-5(\sqrt[]{6})-5(3)
\\\\=
6+3\sqrt[]{6}-5\sqrt[]{6}-15
\\\\=
(6-15)+(3\sqrt[]{6}-5\sqrt[]{6})
\\\\=
-9-2\sqrt[]{6}
.\end{array}