The equation is in the form (x-h)^2 + (y-k)^2 = r^2 where, h = -2.5 = -5/2 k = 0.5 = 1/2 r = sqrt(4.5) = 2.1213 approximately
So that's why the center is (-5/2, 1/2) = (-2.5, 0.5) and the radius is approximately 2.1213 units
note1: I took half of 5 to get 5/2 = 2.5 then I squared it to get (2.5)^2 = 6.25; The value 6.25 is added to both sides. This is done to complete the square for the x terms
note2: Similar to note1, but done for the y terms now. I took half of -1 to get -1/2 = -0.5 and then squared it to get (-0.5)^2 = 0.25, which is added to both sides