Dean's conjecture on cycles divisible by the minimum-degree bound

All graphs under consideration are finite and simple. For a graph $G$ and a vertex $v$, let $d_G(v)$ denote the degree of $v$. Dean's conjecture. For every integer $k \ge 3$, every graph with minimum degree at least $k$ contains a cycle of length divisible by $k$. The conjecture is known to be true for all $k\neq 5$, so the case $k=5$ remains open.