Recent advances in synthesis and characterization methods have enabled the controllable fabrication of atomically precise metal clusters (AMCs) of subnanometer size that possess unique physical and chemical properties, yet to be explored. Such AMCs have potential applications in a wide range of fields, from luminescence and sensing to photocatalysis and bioimaging, making them highly desirable for further research. Therefore, there is a need to develop innovative methods to stabilize AMCs upon surface deposition, as their special properties are lost due to sintering into larger nanoparticles. To this end, dispersion-corrected density functional theory (DFT-D3) and ab initio molecular dynamics (AIMD) simulations have been employed. Benchmarking against high-level post-Hartree-Fock approaches revealed that the DFT-D3 scheme accurately describes the lowest-energy states of clusters of five and ten atoms, Cu5 and Cu10 AIMD simulations performed at 400 K illustrate how intrinsic defects of graphene sheets, carbon vacancies, are capable of confining individual Cu5 clusters, thus allowing for their stabilization. Furthermore, AIMD simulations provide evidence on the dimerization of Cu5 clusters on defect-free graphene, in agreement with the ab initio predictions of (Cu5)10 aggregation in the gas phase. The findings of this study demonstrate the potential of using graphene-based substrates as an effective platform for the stabilization of monodisperse atomically precise Cu5 clusters.