Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 23

$-2i\sqrt{19}+5i\sqrt{5}$

Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $ -\sqrt{-76}+\sqrt{-125} ,$ is equivalent to \begin{array}{l}\require{cancel} -\sqrt{76}\cdot\sqrt{-1}+\sqrt{125}\cdot\sqrt{-1} \\\\= -\sqrt{4\cdot19}\cdot i+\sqrt{25\cdot5}\cdot i \\\\= -\sqrt{(2)^2\cdot19}\cdot i+\sqrt{(5)^2\cdot5}\cdot i \\\\= -2i\sqrt{19}+5i\sqrt{5} .\end{array}