Prove that $x$ has order $5$. let $ x \in G$ such that $(a^{-1})*(x^2)*(a) = x^3$ for some self inverse $a.$ Prove that $x$ has order $5.$
I don't know how to start this proof. Seems really difficult. 

Since there is an answer up, I would do $$ax^2a=x^3$$
$$x^2=a^2x^2a^2=ax^3a=x^3axa$$
$$axa=x^{-1}$$
$$ax^2a=x^{-2}=x^3$$
Leaving you with some bits to fill in.
