By using the center-radius form.
The center is ##C## at ##(h,k)## meaning ##h = -4## and ##k = 2##.
The equation will be ##(x – h)^2 + (y – k)^2 = r^2##
That translates to:
##(x + 4)^2 + (y – 2)^2 = 25##
Expanding, we get
##x^2 + 8x + 16 + y^2 – 4y + 4 = 25##
or
##x^2 + 8x + y^2 – 4y – 5 = 0##
For the graphing part, locate the center ##(-4,2)##. Open your compass 5 units to any direction, then make a circle. It should pass the following points (along with infinitely many other points):
##(-4 + 5, 2)## ##->## ##(1,2)##
##(-4 – 5,2)## ##->## ##(-9, 2)##
##(-4, 2 + 5)## ##->## ##(-4, 7)##
##(-4, 2 – 5)## ##->## ##(-4, -3)##
