The structure of the novel compound La2MoO5 has been solved from powder X-ray and neutron diffraction data and belongs to the tetragonal space group P4/m (no. 83) with a = 12.6847(3) Å and c = 6.0568(2) Å and with Z = 8. It consists of equal proportions of bioctahedral (Mo2O10) and square prismatic (Mo2O8) dimers, both of which contain direct Mo–Mo bonds and are arranged in 1D chains. The Mo–Mo bond length in the Mo2O10 dimers is 2.684(8) Å, while there are two types of Mo2O8 dimers with Mo–Mo bonds lengths of 2.22(2) and 2.28(2) Å. Although the average Mo oxidation state in La2MoO5 is 4+, the very different Mo–Mo distances reflect the fact that the Mo2O10 dimers contain only Mo5+ (d1), while the prismatic Mo2O8 dimers only contain Mo3+ (d3), a result directly confirmed by density function theory calculations. This is due to the complete disproportionation of Mo4+, a phenomenon which has not previously been observed in solid-state compounds. La2MoO5 is diamagnetic, behavior which is not expected for a nonmetallic transition-metal oxide whose cation sites have an odd number of d-electrons. The resistivity displays the Arrhenius-type activated behavior expected for a semiconductor with a band gap of 0.5 eV, exhibiting an unusually small transport gap relative to other diamagnetic oxides. Diffuse reflectance studies indicate that La2MoO5 is a rare example of a stable oxide semiconductor with strong infrared absorbance. It is shown that the d-orbital splitting associated with the Mo2O8 and Mo2O10 dimeric units can be rationalized using simple molecular orbital bonding concepts.