I'm trying to solve this complex number equation: $$z^5=\bar z$$
As far as I understand, every complex number $z$ should be written in trigonometric form: $$r^5(\cos(5\phi) + i\sin(5\phi)) = r(\cos(-\phi) + i\sin(-\phi))$$

Unfortunately, at this moment, I'm stacked. Could you give some ideas that would help me to solve it?