#### Answer

$r=\left\{ 5-2i,5+2i \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To find the non real complex solutions of the given equation, $
(r-5)^2=-4
,$ take the square root of both sides (Square Root Property). Then use the properties of radicals and use $i=\sqrt{-1}.$ Finally, simplify the radical and isolate the variable.
$\bf{\text{Solution Details:}}$
Taking the square root of both sides (Square Root Property), the equation above is equivalent to
\begin{array}{l}\require{cancel}
r-5=\pm\sqrt{-4}
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the equation above is equivalent to\begin{array}{l}\require{cancel}
r-5=\pm\sqrt{-1}\cdot\sqrt{4}
.\end{array}
Using $i=\sqrt{-1},$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
r-5=\pm i\sqrt{4}
.\end{array}
Writing the radicand as an expression that contains a factor that is a perfect power of the given index and then extracting the root of that factor, the equation above is equivalent to
\begin{array}{l}\require{cancel}
r-5=\pm i\sqrt{(2)^2}
\\\\
r-5=\pm i(2)
\\\\
r-5=\pm 2i
.\end{array}
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
r=5\pm 2i
.\end{array}
Hence, $
r=\left\{ 5-2i,5+2i \right\}
.$