We perform spin-polarized density functional theory (DFT) calculations for a hydrogen atom interacting exohedrally with a (5,5) single-walled carbon nanotube (SWNT), and also full 3D quantum dynamics calculations of all H atom bound rovibrational states. A detailed and accurate characterization of the full potential energy surface (PES) requires DFT calculations along a large number of interstitial sites - 18 in all - along 33 separate, non-uniformly spaced radial values are used. The system exhibits a weak physisorptive region between 2.5 and 3.5 angstroms from the SWNT wall (51 meV well depth), and a chemisorptive region between 1.0 and 1.5 angstroms from the SWNT wall (755 meV well depth). A small barrier of +54 meV lies between these two regions, and there are also two distinct transition states that lie between adjacent chemisorptive wells. A subsequent quantum dynamical calculation of all bound rovibrational H atom eigenfunctions and energy levels then reveals interesting ramifications for the use of SWNTs as hydrogen storage devices.