Using the density functional theory, we present a systematic theoretical study of the layer relaxation and surface stress of 5d transition metals. Our calculations predict layer contractions for all surfaces, except for the (111) surface of face centered cubic Pt and Au, where slight expansions are obtained similarly to the case of the 4d series. We also find that the relaxations of the close packed surfaces decrease with increasing occupation number through the 5d series. The surface stress for the relaxed, most closely packed surfaces shows similar atomic number dependence as the surface energy. Using Cammarata's model and our calculated surface stress and surface energy values, we examine the possibility of surface reconstructions, which is in reasonable agreement with the experimental observations.