  We construct explicit consistent Kaluza-Klein reductions of type IIB
supergravity on HK_4 x S^1, where HK_4 is an arbitrary four-dimensional
hyper-Kaehler manifold, and on SE5, an arbitrary five-dimensional
Sasaki-Einstein manifold. In the former case we obtain the bosonic action of
D=5 N=4 (ungauged) supergravity coupled to two vector multiplets. For the SE_5
case we extend a known reduction, which leads to minimal D=5 N=2 gauged
supergravity, to also include a multiplet of massive fields, containing the
breathing mode of the SE_5. We show that the resulting D=5 action is also
consistent with N=4 gauged supergravity coupled to two vector multiplets. This
theory has a supersymmetric AdS_5 vacuum, which uplifts to the class of
supersymmetric AdS_5 x SE_5 solutions, that spontaneously breaks N=4 to N=2,
and also a non-supersymmetric AdS_5 vacuum which uplifts to a class of
solutions first found by Romans.
