  We define some Schnyder-type combinatorial structures on a class of planar
triangulations of the pentagon which are closely related to 5-connected
triangulations. The combinatorial structures have three incarnations defined in
terms of orientations, corner-labelings, and woods respectively. The wood
incarnation consists in 5 spanning trees crossing each other in an orderly
fashion. Similarly as for Schnyder woods on triangulations, it induces, for
each vertex, a partition of the inner triangles into face-connected regions
(5~regions here). We show that the induced barycentric vertex-placement, where
each vertex is at the barycenter of the 5 outer vertices with weights given by
the number of faces in each region, yields a planar straight-line drawing.
