Answer
See below.
Work Step by Step
We can use the distance formula to determine the radius: The distance formula from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
$r=\sqrt{(5-2))^2+(3-(-1))^2}=\sqrt{9+16}=\sqrt{25}=5.$
The general equation for a circle with radius $r$ and centre $(h,k)$ is: $(x-h)^2+(y-k)^2=r^2$, hence our equation: $(x+1)^2+(y-2)^2=5^2$
