Cycles of length divisible by five in graphs of minimum degree five - The k=5 case of Dean's conjecture

We prove that every finite simple graph of minimum degree at least five contains a cycle whose length is divisible by five, settling the remaining case k=5 of Dean’s conjecture. Nine finite configuration propositions in the bipartite and triangle-free branches are computer-assisted. The corresponding verifier sources, certificate data, and reproducibility materials are archived in the computational supplement, version 1.0.1, DOI 10.5281/zenodo.22167084.

Version 1.0.1 supplies a complete two-case argument in the exceptional-leaf boundary-deletion step, covering whether the deletion witness lies on the shortest odd cycle or in its exterior. It also gives exact citations for the tetragonal-core results and normalizes the quoted degree-sum rooted-path theorem to its precise edge-deleted conclusion. No theorem statement, computational predicate, or certificate output is changed. The corresponding computational supplement is version 1.0.1, DOI 10.5281/zenodo.22167084.