#### Answer

$x+2\sqrt{x}-15$

#### Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the FOIL method, and the properties of radicals, the given expression, $
(\sqrt{x}+5)(\sqrt{x}-3)
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{x}(\sqrt{x})+\sqrt{x}(-3)+5(\sqrt{x})+5(-3)
\\\\=
x-3\sqrt{x}+5\sqrt{x}-15
\\\\=
x+2\sqrt{x}-15
.\end{array}
Note that all variables represent positive real numbers.