Find the image of the following region

under the action of $\displaystyle f(z)=z^5$.

I am horrible with mappings. I wrote $\displaystyle z^5=r^5 \cdot e^{5i\theta_0}$, and tried points in both regions, and then I ended up with the whole complex plane as the output and I don't think this is right. How do I find the image of this region? Thanks for the help.