The N=2, D=5 gauge supergravity theory has attracted a lot of interest due to AdS/CFT and Randall-Sundrum scenarios, as it is the most general supergravity with the minimal amount of supersymmetry in five spacetime dimensions. The study of its BPS solutions which preserve part of the supersymmetry are of chiefly interest in this contest. This work is recognized in the literature as the first attempt of classifying BPS solutions in presence of hypermultiplet couplings.