The general equation of a circle is:

where:
(a, b) = coordinates of the center of the circle
r = radius of the circle
Now, the equation given in the question, which is:

Can be re-written as follows:

Now, we can easily compare the resulting expression with the general equation of a circle.
On doing so, we have that:
(a, b) = (-5, 4)
r = 3
Thus, the center of the circle is (-5, 4) and the radius is 3
Therefore, the correct answer is: Option C