Answer
{$5+2i,5-2i$}
Work Step by Step
Given: $(x-5)^2=-4$
Apply The Square Root Property.
This can be written as: $x-5=\sqrt{-4}$
As we know that $\sqrt{-1}=i$]
or, $x-5=\pm 2i$
or, $x=5+2i,5-2i$
Hence, solution set is $x=${$5+2i,5-2i$}