Altermagnets are compensated magnets belonging to spin symmetry groups that allow alternating spin polarizations both in the coordinate space of the crystal and in the momentum space of the electronic structure. In these materials the anisotropic local crystal environment of the different sublattices lowers the symmetry of the system so that the opposite-spin sublattices are connected only by rotations. This results in an unconventional spin-polarized band structure in the momentum space. This low symmetry of the crystal structure is expected to be reflected in the anisotropy of the anomalous Hall effect. In this work, we study the anisotropy of the anomalous Hall effect in epitaxial thin films of Mn5Si3, an altermagnetic candidate material. We first demonstrate a change in the relative Néel vector orientation when rotating the external field orientation through systematic changes in both the anomalous Hall effect and the anisotropic longitudinal magnetoresistance. We then show that the anomalous Hall effect in this material is anisotropic with the Néel vector orientation relative to the crystal structure and that this anisotropy requires high crystal quality and unlikely stems from the magnetocrystalline anisotropy. Our results thus provide further systematic support to the case for considering epitaxial thin films of Mn5Si3 as an altermagnetic candidate material.