Where is the fault in my proof? I had some spare time, so I was just doing random equations, then accidentally came up with a proof that showed that i was -1. I know this is wrong, but I can't find where I went wrong. Could someone point out where a mathematical error was made?
$$(-1)^{2.5}=-1\\
(-1)^{5/2}=-1\\
(\sqrt{-1})^5=-1\\
i^5=-1\\
i=-1$$

$$(-1)^{2.5} =(-1)^2\times (-1)^{1/2}= \sqrt{(-1)} =  i$$ is your mistake
