The equation of a circle is
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center
and r is the radius
(-4, 2) being the center
and r = 5
means that
h = -4
k = 2
r = 5
so
(x - (-4))^2 + (y - 2)^2 = (5)^2
simplified
(x + 4)^2 + (y - 2)^2 = 25
Therefore your answer is C.