#### Answer

$2+2i\sqrt{2}$

#### Work Step by Step

Original Problem:
$\frac{10 + \sqrt{-200}}{5}$
Factor out $\sqrt{-1}$ and 10 from $\sqrt{-200}$.
$\frac{10+\sqrt{-1}\times10\sqrt{2}}{5}$
Recall that $\sqrt{-1}$ = $i$.
$\frac{10+10i\sqrt{2}}{5}$
Divide each numerator term by 5.
$2+2i\sqrt{2}$