The structure of the disordered lanthanum molybdate, LaMo2O5, has been solved and refined using powder neutron diffraction data collected at 300 K. The average structure is described in P6(3)/mmc, a = 8.373(1) Angstrom, c = 19.1510(1) Angstrom, Z = 12. The compound contains two types of Mo-Mo bonded units: isolated octahedral Mo6O18 clusters, and infinite molybdenum oxide sheets, formed from condensed triangular Mo3O13 clusters joined together to give a total of four Mo-Mo bonds for each molybdenum. The Mo6O18 clusters have 16 electrons available for metal-metal bonding and the Mo-Mo distances within the unit are 2.643(4) Angstrom x 6 and 2.695(5) Angstrom x 6. In the infinite sheets the molybdenum-molybdenum distances are 2.612(9) Angstrom within one equilateral triangular cluster and 2.621(8) Angstrom within another. Each of the molybdenum atoms in the two different Mo-3 clusters has two molybdenum neighbors from the other cluster at a distance of 2.882(6) Angstrom. Disorder in this layered structure occurs because of interchange of layers of Mo sheets with layers of lanthanum ions. The Bragg scattering is accounted for by including layers occupied with a 50% probability by each of these structural elements and their associated oxygen atoms. A model showing how ordered subunits are stacked together to produce the average structure is presented. Extended X-ray absorption fine structure spectroscopy (EXAFS) at the Mo K-edge was used to give information on the local structure around molybdenum and to confirm that the final structural model gives a good description of Mo-O and Mo-Mo bonding.