This article is a part of our efforts to control the magnetic anisotropy in cyanide-based exchange-coupled systems with the eventual goal to obtain single-molecule magnets with higher blocking temperatures. We give the theoretical interpretation of the magnetic properties of the new pentanuclear complex {[Ni-II(tmphen)(2)](3)[Os-III(CN)(6)](2)}center dot 6CH(3)CN ((Ni3Os2III)-Os-II cluster). Because the system contains the heavy Os-III ions, spin-orbit coupling considerably exceeds the contributions from the low-symmetry crystal field and exchange coupling. The magnetic properties of the (Ni3Os2III)-Os-II cluster are described in the framework of a highly anisotropic pseudo-spin Hamiltonian that corresponds to the limit of strong spin-orbital coupling and takes into account the complex molecular structure. The model provides a good fit to the experimental data and allows the conclusion that the trigonal axis of the bipyramidal (Ni3Os2III)-Os-II cluster is a hard axis of magnetization. This explains the fact that in contrast with the isostructural trigonal bipyramidal (Mn2Mn3II)-Mn-III cluster, the (Ni3Os2III)-Os-II system does not exhibit the single-molecule magnetic behavior.