number theory - Congruence in $mathbb{Z}_5[x]$

I'm not really sure how to approach this problem, since it doesn't seem similar to solving linear congruences in $\mathbb{Z}_m$.

Find all solutions in $\mathbb{Z}_5[x]$ to the congruence $(x^2-1)a(x)\equiv x^2+x-2\pmod{x^3-1}$. Additionally, is it possible to count the number of solutions in $(\mathbb{Z}_5[x])_{x^3-1}$ without actually finding them?

Any help is appreciated.