Invariant Rings of Adjacent-Quadratic Triangular Derivations

Let $k$ be a field of characteristic zero and $D_5$ the triangular locally nilpotent derivation $D_5(a_n)=a_{n+1}a_{n+2}$ on $A_5=k[a_0,\dots,a_5]$. We prove $A_5^{D_5} = C_5[F_{46}^{\mathrm{int}}],$ hence finitely generated, where $C_5=k[p,q,J_1,J_2,F_0,H]$ is the normal hypersurface $q^4H-11025F_0