  For a planar graph $G$, Borodin stated that $G$ is
$(\Delta+1)$-edge-choosable if $\Delta \geq9$ and later Bonamy showed that $G$
is $9$-edge-choosable if $\Delta=8$. At the same time, Borodin et al. proved
that $G$ is $\Delta$-edge-choosable if $\Delta\geq12$. In the paper, we extend
these results to $K_5$-minor free graphs.
