Packing solid shapes into regular lattices can yield very complex assemblies, not all of which achieve the highest packing fraction. In two dimensions, the regular pentagon is paradigmatic, being the simplest shape that does not pave the plane completely. In this work, we demonstrate the packing of plasmonic nanoprisms with pentagonal cross section, which form extended supercrystals. We do encounter the long-predicted ice-ray and Dürer packings (with packing fractions of 0.921 and 0.854, respectively), but also a variety of novel polymorphs that can be obtained from these two configurations by a continuous sliding transformation and exhibit an intermediate packing fraction. Beyond the fundamental interest of this result, fine control over the density and symmetry of such plasmonic assemblies opens the perspective of tuning their optical properties, with potential applications in metamaterial fabrication, catalysis or molecular detection.