How can one split these kind of rings as a direct sum of minimal ideals

Question

Let $P = \Bbb Q[x,y,z,u,v]$ and $I$ the ideal generated by: $$\begin{cases} x^5-2x^4+2x^3-x^2+1,\\ x^4+x^3y+x^2y^2+xy^3+y^4-2x^3-2x^2y-2xy^2-2y^3+2x^2+2xy+2y^2-x-y,\\ x^3+x^2y+x^2z+xy^2+xyz+xz^2+y^3+y^2z+yz^2+z^3-2x^2-2xy-2xz-2y^2-2yz-2z^2+2x+2y+2z-1,\\ x^2+xy+xz+xu+y^2+yz+yu+z^2+zu+u^2-2x-2y-2z-2u+2,\\ x+y+z+u+v-2\end{cases} $$ How can I split $P/I$ as a direct sum of minimal ideals? I solved this question using a matrix algebra that is isomorphic to $P/I$ but I want to know if there is a solution using only polynomials.