Least dense hyperball covering conjecture for the Coxeter tiling $[5,3,3,3,3]$

Let $\mathbf{H}^5$ be the 5-dimensional hyperbolic space, and consider the Coxeter tiling $[5,3,3,3,3]$ and the hyperball covering described in the paper. Least dense hyperball covering conjecture. The above described hyperball covering to Coxeter tiling $[5,3,3,3,3]$ provides the least dense hyperball covering in $\mathbf{H}^5$. This conjecture concerns the optimal density among hyperball coverings associated with the relevant Coxeter tilings; the supplied text does not state whether it has been proved or disproved.