In one circle there will be five roots, all evenly spaced around a circle, so having the same magnitude and separated by the same angle $\displaystyle \displaystyle \frac{2\pi}{5}$

$\displaystyle \displaystyle \begin{align*} z^5 &= i \\ z^5 &= e^{\frac{\pi}{2}i} \\ z &= \left( e^{\frac{\pi}{2}i} \right) ^{\frac{1}{5}} \\ z &= e^{\frac{\pi}{10}i} \end{align*}$

So the first of these roots is $\displaystyle \displaystyle \begin{align*} z = e^{\frac{\pi}{10}i} \end{align*}$, and the rest are separated by an angle of $\displaystyle \displaystyle \begin{align*} \frac{2\pi}{5} \end{align*}$, so in the region $\displaystyle \displaystyle \begin{align*} \left( \pi , \pi \right] \end{align*}$ we have

$\displaystyle \displaystyle \begin{align*} z &= \left\{ e^{-\frac{7\pi}{10}i} , e^{-\frac{3\pi}{10}i} , e^{\frac{\pi}{10}i} , e^{\frac{\pi}{2}i}, e^{\frac{9\pi}{10}i} \right\} \end{align*}$

Of course, all multiples of $\displaystyle \displaystyle \begin{align*} 2\pi \end{align*}$ will also work.