  A proper coloring of a graph is odd if every non-isolated vertex has some
color that appears an odd number of times on its neighborhood. Petru\v{s}evski
and \v{S}krekovski conjectured in 2021 that every planar graph admits an odd
$5$-coloring. We confirm this conjecture for outer-1-planar graphs and
2-boundary planar graphs, which are two subclasses of planar graphs.
