Chapter R - Section R.3 - Exponents, Roots, and Order of Operations - R.3 Exercises - Page 30: 73

$-2$

Using order of operations and the properties of radicals, the given expression, $ \dfrac{(-5+\sqrt{4})(-2^2)}{-5-1} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{(-5+2)(-4)}{-6} \\\\= \dfrac{(-3)(\cancel{-4}^2)}{\cancel{-6}^3} \\\\= \dfrac{-6}{3} \\\\= -2 .\end{array}