The hexavalent and heptavalent sodium neptunate compounds Na4NpO5 and Na5NpO6 have been investigated using X-ray powder diffraction, Mössbauer spectroscopy, magnetic susceptibility, and specific heat measurements. Na4NpO5 has tetragonal symmetry in the space group I4/m, while Na5NpO6 adopts a monoclinic unit cell in the space group C2/m. Both structures have been refined for the first time using the Rietveld method. The valence states of neptunium in these two compounds, i.e., Np(VI) and Np(VII), respectively, have been confirmed by the isomer shift values of their Mössbauer spectra. The local structural properties obtained from the X-ray refinements have also been related to the quadrupole coupling constants and asymmetry parameters determined from the Mössbauer studies. The absence of magnetic ordering has been confirmed for Na4NpO5. However, specific heat measurements at low temperatures have suggested the existence of a Schottky-type anomaly at around 7 K in this Np(VI) phase.