Zirconium pentatelluride was recently reported to be a 3D Dirac semimetal, with a single conical band, located at the center of the Brillouin zone. The cone's lack of protection by the lattice symmetry immediately sparked vast discussions about the size and topological or trivial nature of a possible gap opening. Here, we report on a combined optical and transport study of ZrTe5, which reveals an alternative view of electronic bands in this material. We conclude that the dispersion is approximately linear only in the a-c plane, while remaining relatively flat and parabolic in the third direction (along the b axis). Therefore, the electronic states in ZrTe5 cannot be described using the model of 3D Dirac massless electrons, even when staying at energies well above the band gap 2 Delta = 6 meV found in our experiments at low temperatures.