1. The problem statement, all variables and given/known data Let G be a group with identity e. Let a and b be elements of G with a≠e, b≠e, (a^5)=e, and (aba^-1)=b^2. If b≠e, find the order of b. 2. Relevant equations Maybe the statement if |a|=n and (a^m)=e, then n|m. Other ways of writing (aba^-1)=b^2: ab=(b^2)a b=(a^-1)(b^2)a a=(b^2)a(b^-1) Also, if the order of a=5, then |a|=|(b^2)a(b^-1)|=5 3. The attempt at a solution My work is kinda in the relevant equations. I have manipulated the given formula and looked at the statement listed above but can't see if these will get me anywhere or started in the right direction.