In this work, we investigate five-dimensional scale-dependent black hole solutions by modelling their event horizon with some of the eight Thurston three-dimensional geometries. Specifically, we construct constant curvature scale-dependent black holes and also the more exotic scale-dependent Solv black hole. These new solutions are obtained by promoting both the gravitational and the cosmological couplings to r-dependent functions, in light of a particular description of the effective action inspired by the high energy philosophy. Interestingly, the so-called run-ning parameter, together with the topology of the event hori-zon, control the asymptotic structure of the solutions found. Finally, differences in both the entropy and the temperature between the classical and the scale-dependent Solv black hole are briefly commented.