#### Answer

$\dfrac{170}{13}$

#### 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{5p+6r^2}{p^2+q-1}
.$
$\bf{\text{Solution Details:}}$
Substituting $p=-4,q=-2,$ and $r=5,$ the given expression evaluates to
\begin{array}{l}\require{cancel}
\dfrac{5(4)+6(5)^2}{(-4)^2+(-2)-1}
.\end{array}
Simplifying the expressions in parenthesis and simplifying the exponents, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{5(4)+6(25)}{16-2-1}
.\end{array}
Simplifying the products, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{20+150}{16-2-1}
.\end{array}
Simplifying the sums/differences, the expression above becomes
\begin{array}{l}\require{cancel}
\dfrac{170}{13}
.\end{array}