  We classify the supersymmetric vacua of N=4, d=5 supergravity in terms of
G-structures. We identify three classes of solutions: with R^3, SU(2) and
generic SO(4) structure. Using the Killing spinor equations, we fully
characterize the first two classes and partially solve the latter. With the N=4
graviton multiplet decomposed in terms of N=2 multiplets: the graviton, vector
and gravitino multiplets, we obtain new supersymmetric solutions corresponding
to turning on fields in the gravitino multiplet. These vacua are described in
terms of an SO(5) vector sigma-model coupled with gravity, in three or four
dimensions. A new feature of these N=4 vacua, which is not seen from an N=2
point of view, is the possibility for preserving more exotic fractions of
supersymmetry. We give a few concrete examples of these new supersymmetric
(albeit singular) solutions. Additionally, we show how by truncating the N=4,
d=5 set of fields to minimal supergravity coupled with one vector multiplet we
recover the known two-charge solutions.
