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In this work, we investigate five-dimensional scale-dependent black holesolutions by modelling their event horizon with some of the eight Thurstonthree-dimensional geometries. Specifically, we construct constant curvaturescale-dependent black holes and also the more exotic scale-dependent Solv blackhole. These new solutions are obtained by promoting both the gravitational andthe cosmological couplings to $r$-dependent functions, in light of a particulardescription of the effective action inspired by the high energy philosophy.Interestingly, the so-called running parameter, together with the topology ofthe event horizon, control the asymptotic structure of the solutions found.Finally, differences in both the entropy and the temperature between theclassical and the scale-dependent Solv black hole are briefly commented.

Five-dimensional scale-dependent black holes with constant curvature and Solv horizons