x^2 + ( y + 5)^2 = 25
x = r cos θ
y = r sin θ
So we have
(r cos θ)^2 + (r sin θ + 5)^2 = 25
r^2 cos^2 θ + r^2 sin^2 θ + 10r sin θ + 25 = 25
r^2 ( cos ^2 θ + sin^2 θ ) + 10rsin θ = 0
r^2 ( 1) + 10r sin θ = 0
r^2 + 10r sin θ = 0 divide out r
r +10 sin θ = 0
r = -10 sin θ