Hanauer's feedback arc set conjecture for degree-five oriented multigraphs

Let $D$ be an oriented multigraph, and write $\Delta$ for its maximum degree. A feedback arc set is a set of arcs whose deletion makes $D$ acyclic; let ${\rm fas}(D)$ denote its minimum size. Let $n$ be the number of vertices.

Hanauer's conjecture. If $\Delta\leq 5$, then

$${\rm fas}(D)\leq \frac{2.5n}{3}.$$

Hanauer posed this as a bounded-degree upper bound for the minimum feedback arc set. The conjecture is solved by the paper's main theorem, which establishes the stronger estimate ${\rm fas}(D)\leq m/3$; since $\Delta\leq 5$ implies $m\leq 2.5n$, the conjectured bound follows.