In this paper we present a microscopic model for the cooperative spin-crossover (SCO) phenomenon in crystals containing cyano-bridged pentanuclear clusters {[M^III(CN)₆]₂[M ^II(tmphen)₂]₃} (M/M= Co/Fe, 1; Fe/Fe, 2) with a trigonal bipyramidal (TBP) structure. The low-spin to high-spin (ls-hs) transition is considered as a cooperative phenomenon that is driven by the interaction of electronic shells of Fe^II ions with totally symmetric deformation of the local environment that is extended over the crystal lattice via the acoustic phonon field. Due to proximity of Fe^II ions in the cluster, the short-range intracluster interaction between these ions via the optical phonon field is included as well. The model takes into consideration also the spin-orbit coupling operating within the cubic ⁵T ₂(t₂4e²) term of the hs-Fe^II ions. For cluster 2 the Heisenberg-type exchange interaction between the hs-Fe ^II and ls-Fe^III ions is taken into account. The competition between short- and long-range interactions is shown to determine the type and temperature of the SCO transition in cluster systems. The proposed model explains, in a unique way, the temperature dependence of the static magnetic susceptibility and the Mössbauer spectra of the title compounds. The approach described in this paper represents a theoretical tool for the study of spin-crossover systems based on metal clusters.