We perform density functional theory calculations using Gaussian atomic-orbital methods within the generalized gradient approximation for the exchange and correlation to study the interactions in the bare and hydrogenated platinum clusters. The minimum-energy structures, binding energies, relative stabilities, vibrational frequencies and the highest occupied and lowest unoccupied molecular-orbital gaps of Pt n H m (n=1-5, m=0-2) clusters are calculated and compared with previously studied pure platinum and hydrogenated platinum clusters. We investigate any magic behavior in hydrogenated platinum clusters and find that Pt 4 H 2 is more stable than its neighboring sizes. Our results do not agree with a previous conclusion that 3D geometries of Pt tetramer and pentamer are unfavored. On the contrary, the lowest energy structure of Pt 4 is found to be a distorted tetrahedron and that of Pt 5 is found to be a bridge site capped tetrahedron which is a new global minimum for Pt 5 cluster. The successive addition of H atoms to Pt n clusters leads to an oscillatory change in the magnetic moment of Pt 3 -Pt 5 clusters.