The property $R_\infty$ conjecture for the Artin group of type $D_5$

Let $A[D_5]$ be the Artin group of spherical type $D_5$, and let $Z(A[D_5])$ denote its center. The $D_5$ property $R_\infty$ conjecture. The Artin group $A[D_5]$ and its central quotient

$$A[D_5]/Z(A[D_5])$$

also have property $R_\infty$. The cases of type $D_n$ for $n\geqslant 6$ and type $D_4$ are known, leaving $A[D_5]$ as the only unresolved case in this series.