Quantum-mechanical calculations of the potential energy curves of the singlet and triplet states of LiH, NaH, KH, RbH, and CsH formed by the approach of ground state alkali-metal atoms and hydrogen atoms are presented. Precise values are determined for the coefficients of the van der Waals interaction and estimates are made of the contribution of the exchange interaction at large distances. Together with empirical data, they are used to assess and improve the accuracy of the ab initio potentials.