Hydrogen storage is among the most demanding challenges in the hydrogen-based energy cycle. One proposed strategy for hydrogen storage is based on physisorption on high surface area solids such as metal-organic frameworks (MOFs). Within this class of materials, MOF-5 has been the first structure studied for hydrogen storage. The IR spectroscopy of adsorbed H2 performed at 15 K and ab initio calculations show that the adsorptive properties of this material are mainly due to dispersive interactions with the internal wall structure and to weak electrostatic forces associated with O13Zn4 clusters. Calculated and measured binding enthalpies are between 2.26 and 3.5 kJ/mol, in agreement with the H2 rotational barriers reported in the literature. A minority of binding sites with higher adsorption enthalpy (7.4 kJ/mol) is also observed. These species are probably associated with OH groups on the external surfaces present as termini of the microcrystals.