Abstract Novel highly selective synthesis techniques have enable the production of atomically precise monodisperse metal clusters (AMCs) of subnanometer size. These AMCs exhibit ‘molecule‐like’ structures that have distinct physical and chemical properties, significantly different from those of nanoparticles and bulk material. In this work, we study copper pentamer Cu 5 clusters as model AMCs by applying both density functional theory (DFT) and high‐level (wave‐function‐based) ab initio methods, including those which are capable of accounting for the multi‐state multi‐reference character of the wavefunction at the conical intersection (CI) between different electronic states and augmenting the electronic basis set till achieving well‐converged energy values and structures. After assessing the accuracy of a high‐level multi‐multireference ab initio protocol for the well‐known Cu 3 case, we apply it to demonstrate that bypiramidal Cu 5 clusters are distorted Jahn‐Teller (JT) molecules. The method is further used to evaluate the accuracy of single‐reference approaches, finding that the coupled cluster singles and doubles and perturbative triples CCSD(T) method delivers the results closer to our ab initio predictions and that dispersion‐corrected DFT can outperform the CCSD method. Finally, we discuss how JT effects and, more generally, conical intersections, are intimately connected to the fluxionality of AMCs, giving them a ‘floppy’ character that ultimately facilitates their interaction with environmental molecules and thus enhances their functioning as catalysts.