Order of an element in $F_2[X]/X^5+X^2+1$

Question

Let $Q=X^5+X^2+1 \in F_2[X]$. Q is irreducible.

Let $K=F_2[X]/Q$.

Let $\alpha$ be the class of $X$ in $K$.

I am trying to find the inverse of $\alpha$ in $K$.

What I did:

I am new to finite fields theory so I tried to understand $\alpha$.

$\alpha \in \overline{X}$ means $X-\alpha \in I_\alpha=\{P\in K[X]: P(\alpha)=0\}$. Is that accurate?

I know also from my course that $(1, \alpha, . . . , \alpha^4 )$ is a basis of K so $|K|= 2^5$.

I don't know how to follow-up. any help much appreciated. Thanks!