4-coloring maps of pentagons

If $v$ is a vertex of degree at most 4 in a planar graph $G$ then one can extend a proper 4-coloring of $V(G) \setminus \{v\}$ to $v$ after possibly modifying it using the classical Kempe chain argument. See for example paragraph 5 of the "Summary of proof ideas" section of the Wikipedia entry on the 4-color theorem: http://en.wikipedia.org/wiki/Four_color_theorem

As pentagons with exposed edges correspond to vertices of degree 4 in the dual graph, one can color the map by induction using this trick.