We explore the transition to a charge-disproportionated insulating phase in a five-orbital cubic tight-binding model applicable to transition-metal perovskites with a formal d^4 occupation of the transition-metal cation, such as ferrates or manganites. We use dynamical mean-field theory to obtain the phase diagram as a function of the average local Coulomb repulsion U and the Hund's coupling J. The main structure of the phase diagram follows from the zero band-width (atomic) limit and represents the competition between high-spin and low-spin homogeneous and an inhomogeneous charge-disproportionated state. This results in two distinct insulating phases: the standard homogeneous Mott insulator and the inhomogeneous charge-disproportionated insulator, recently also termed Hund's insulator. We characterize the unconventional nature of this Hund's insulating state. Our results are consistent with previous studies of two- and three-orbital models applicable to isolated t2g and eg subshells, respectively, with the added complexity of the low-spin/high-spin transition. We also test the applicability of an effective two-orbital (eg-only) model with disordered S=3/2 t2g core spins. Our results show that the overall features of the phase diagram in the high-spin region are well described by this simplified two-orbital model but also that the spectral features exhibit pronounced differences compared to the full five-orbital description.