For He-3-CO and He-4-CO van der Waals bimers, fully resolved infrared spectra in the 4.7 mu m region near the fundamental band origin of the CO monomer have been measured for the first time. Only a small fraction of the observed lines could be assigned using conventional empirical spectroscopic techniques, and little additional insight was gained from synthetic spectra generated from a published ab initio potential for this system. However, a complete set of unique assignments was made on the basis of comparisons with synthetic spectra generated from a variety of trial potential energy surfaces, and least-squares fits to the observed transition frequencies were used to determine a new anisotropic potential energy surface for this system. This new surface is much deeper and has a much stronger well depth anisotropy than the best previous one, and its predictions of very low temperature microwave line broadening cross sections raise serious questions regarding the methodology for calculating that property.