Inelastic H(2):He collisions are studied from the experimental and theoretical points of view between 22 and 180 K. State-to-state cross sections and rates are calculated at the converged close-coupling level employing recent potential energy surfaces (PES): The MR-PES [J. Chem. Phys. 100, 4336 (1994)], and the MMR-PES and BMP-PESs [J. Chem. Phys. 119, 3187 (2003)]. The fundamental rates k(2-->0) and k(3-->1) for H(2):He collisions are assessed experimentally on the basis of a master equation describing the time evolution of rotational populations of H(2) in the vibrational ground state. These populations are measured in the paraxial region of supersonic jets of H(2)+He mixtures by means of high-sensitivity and high spatial resolution Raman spectroscopy. Good agreement between theory and experiment is found for the k(2-->0) rate derived from the MR-PES, but not for the BMP-PES. For the k(3-->1) rate, which is about one-third to one-half of k(2-->0), the result is less conclusive. The experimental k(3-->1) rate is compatible within experimental error with the values calculated from both PESs. In spite of this uncertainty, the global consistence of experiment and theory in the framework of Boltzmann equation supports the MR-PES and MMR-PESs, and the set of gas-dynamic equations employed to describe the paraxial region of the jet at a molecular level.