We report rigorous quantum five-dimensional (5D) calculations of the coupled translation-rotation (T-R) eigenstates of a H 2 molecule adsorbed in metal organic framework-5 (MOF-5), a prototypical nanoporous material, which was treated as rigid. The anisotropic interactions between H 2 and MOF-5 were represented by the analytical 5D intermolecular potential energy surface (PES) used previously in the simulations of the thermodynamics of hydrogen sorption in this system [Belof, J. Phys. Chem. C 113, 9316 (2009)10.1021/jp901988e]. The global and local minima on this 5D PES correspond to all of the known binding sites of H 2 in MOF-5, three of which, α-, β-, and γ-sites are located on the inorganic cluster node of the framework, while two of them, the δ- and -sites, are on the phenylene link. In addition, 2D rotational PESs were calculated ab initio for each of these binding sites, keeping the center of mass of H 2 fixed at the respective equilibrium geometries; purely rotational energy levels of H 2 on these 2D PESs were computed by means of quantum 2D calculations. On the 5D PES, the three adjacent γ-sites lie just 1.1 meV above the minimum-energy α-site, and are separated from it by a very low barrier. These features allow extensive wave function delocalization of even the lowest translationally excited T-R eigenstates over the α- and γ-sites, presenting significant challenges for both the quantum bound-state calculations and the analysis of the results. Detailed comparison is made with the available experimental data.