We construct and study the first supersymmetric black-hole solutions of non-Abelian-gauged N = 1, d = 5 supergravity ( N = 1, d = 5 SuperEinstein-Yang-Mills theory) with non-trivial SU(2) gauge fields: BPST instantons for black holes and BPS monopoles of different kinds ('t Hooft-Polyakov, Wu-Yang and Protogenov) for certain black holes that are well defined solutions only for very specific values of all the moduli. Instantons do not contribute to the masses but do contribute to the entropies. \par The construction is based on the existant characterization of the supersymmetric solutions of gauged N = 1, d = 5 supergravity coupled to vector multiplets, which we elaborate upon by finding the rules to construct supersymmetric solutions with one additional isometry. These rules automatically connect the non-Abelian supersymmetric solutions of N = 1, d = 5 SEYM theory with the ones of N = 2, d = 4 SEYM theory by dimensional reduction and oxidation. The singular Kronheimer reduction of instantons to colored monopoles we recently discovered plays a crucial role in this relation.