  With the general aim to classify BPS solutions in N=2, D=5 supergravities
interacting with an arbitrary number of vector, tensor and hypermultiplets,
here we begin considering the most general electrostatic, spherical-symmetric
BPS solutions in the presence of hypermultiplet couplings. We discuss the
properties of the BPS equations and the restrictions imposed by their
integrability conditions. We exhibit explicit solutions for the case of static
BPS black-holes coupled to one (the so called universal) hypermultiplet.
