  Thomassen in 1994 published a famous proof of the fact that the choosability
of a planar graph is at most 5. Zhu in 2019 generalized this result by showing
that the same bound holds for Alon-Tarsi numbers of planar graphs. We present
an alternative proof of that fact, derived from the results on decompositions
of planar graphs into trees known as Schnyder woods. It turns out that
Thomassen's technique and our proof based on Schnyder woods have a lot in
common. We discuss and explain the prominent role that counterclockwise
3-orientations play in proofs based on both these approaches.
