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) angstrom and c = 6.0568(2)angstrom 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) angstrom, while there are two types of Mo2O8 dimers with Mo-Mo bonds lengths of 2.22(2) and 2.28(2) angstrom. 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+ (d(1)), while the prismatic Mo2O8 dimers only contain Mo3+ (d(3)), 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.