#### Answer

$-5i\sqrt{3}$

#### Work Step by Step

Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $
-\sqrt{-75}
,$ is equivalent to
\begin{array}{l}\require{cancel}
-\sqrt{75}\cdot\sqrt{-1}
\\\\=
-\sqrt{25\cdot3}\cdot i
\\\\=
-\sqrt{(5)^2\cdot3}\cdot i
\\\\=
-5i\sqrt{3}
.\end{array}