We classify the supersymmetric solutions of ungauged N=1 d=5 SUGRA coupled to
vector multiplets and hypermultiplets. All the solutions can be seen as
deformations of solutions with frozen hyperscalars. We show explicitly how the
5-dimensional Reissner-Nordstrom black hole is deformed when hyperscalars are
living on SO(4,1)/SO(4) are turned on, reducing its supersymmetry from 1/2 to
1/8. We also describe in the timelike and null cases the solutions that have
one extra isometry and can be reduced to N=2,d=4 solutions. Our formulae allows
the uplifting of certain N=2,d=4 black holes to N=1,d=5 black holes on KK
monopoles or to pp-waves propagating along black strings.Comment: Some typos fixed and some paragraphs improved. 44 pages, Latex 2e
file, no figures. Version to be published in JHE