  We demonstrate that random tensors transforming under rank-$5$ irreducible
representations of $\mathrm{O}(N)$ can support melonic large $N$ expansions.
Our construction is based on models with sextic ($5$-simplex) interaction,
which generalize previously studied rank-$3$ models with quartic (tetrahedral)
interaction (arXiv:1712.00249 and arXiv:1803.02496). Beyond the irreducible
character of the representations, our proof relies on recursive bounds derived
from a detailed combinatorial analysis of the Feynman graphs. Our results
provide further evidence that the melonic limit is a universal feature of
irreducible tensor models in arbitrary rank.
