Let $z$ be a nonreal complex number.  Find the smallest possible value of
\[\frac{\text{Im}(z^5)}{[\text{Im}(z)]^5}.\]Note: For a complex number $z,$ $\text{Im}(z)$ denotes the imaginary part of $z.$
<|im_start|>system
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<|im_start|>user
Let $z$ be a nonreal complex number.  Find the smallest possible value of
\[\frac{\text{Im}(z^5)}{[\text{Im}(z)]^5}.\]Note: For a complex number $z,$ $\text{Im}(z)$ denotes the imaginary part of $z.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-4
Let $z$ be a nonreal complex number.  Find the smallest possible value of
\[\frac{\text{Im}(z^5)}{[\text{Im}(z)]^5}.\]Note: For a complex number $z,$ $\text{Im}(z)$ denotes the imaginary part of $z.$
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