The magnetic properties of X/5Fe/X (X: Hf, Ta, W, Re, Os, Ir, Pt) have been studied by means of the full-potential linearized augmented-plane-wave method, in which the core states are treated fully relativistically and the valence states are treated semirelativistically and the generalized gradient approximations' (GCA) exchange-correlation potentials are employed for 5d elements. It has been found that Hf, Ta, W, Re and Os overlayers on Fe(0 0 1) are almost nonmagnetic. Following this trend, if the spin-orbit interactions are taken into account, the magnetism of Ir and Pt overlayers is expected to be killed as for the Ag(0 0 1) and Au(0 0 1) substrate. So the nonexistence of the magnetism for 5d overlayers is furtherly verified on ferromagnetic substrate besides on nonmagnetic substrate. Moreover, due to the more extended 5d orbitals as compared to those of 3d and 4d, much stronger hybridizations between the 5d states of the overlayer and the Fe substrate exist, which greatly suppress the magnetic moment of the interface Fe layer.