#### Answer

$\text{undefined}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Substitute the given value of the variables and then use the order of operations (PEMDAS - Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction) to evaluate the given expression, $
\dfrac{\sqrt{r}}{-p+2q}
.$
$\bf{\text{Solution Details:}}$
Substituting $p=-4,q=-2,$ and $r=5,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{5}}{-(-4)+2(-2)}
.\end{array}
Simplifying the expressions in parenthesis, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{5}}{4+2(-2)}
.\end{array}
Simplifying the products, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{5}}{4-4}
.\end{array}
Simplifying the sums/differences, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{5}}{0}
.\end{array}
Since division by zero is not allowed, then the value of the given expression is $
\text{undefined}
.$