#### Answer

$9\frac{1}{2}\sqrt5$

#### Work Step by Step

$-\frac{1}{2}\sqrt5+2\sqrt{125}\longrightarrow$ factor the perfect square out of 125
=$-\frac{1}{2}\sqrt5+2\sqrt{25\times5}\longrightarrow$ multiplication property of square roots
=$-\frac{1}{2}\sqrt5+2(\sqrt{25})(\sqrt5)\longrightarrow$ simplify
=$-\frac{1}{2}\sqrt5+2(5)(\sqrt5)\longrightarrow$ multiply
=$-\frac{1}{2}\sqrt5+10\sqrt5\longrightarrow$ use distributive property
=$\sqrt5(-\frac{1}{2}+10)\longrightarrow$ simplify
=$9\frac{1}{2}\sqrt5$