  In this paper we study congruent and non-congruent hyperball (hypersphere)
packings of the truncated regular tetrahedron tilings. These are derived from
the Coxeter simplex tilings $\{p,3,3\}$ $(7\le p \in \mathbb{N})$ and
$\{5,3,3,3,3\}$ in $3$ and $5$-dimensional hyperbolic space. We determine the
densest hyperball packing arrangements related to the above tilings. We find
packing densities using congruent hyperballs and determine the smallest density
upper bound of non-congruent hyperball packings generated by the above tilings.
