We construct the general form of matter coupled N=4 gauged supergravity in
five dimensions. Depending on the structure of the gauge group, these theories
are found to involve vector and/or tensor multiplets. When self-dual tensor
fields are present, they must be charged under a one-dimensional Abelian group
and cannot transform non-trivially under any other part of the gauge group. A
short analysis of the possible ground states of the different types of theories
is given. It is found that AdS ground states are only possible when the gauge
group is a direct product of a one-dimensional Abelian group and a semi-simple
group. In the purely Abelian, as well as in the purely semi-simple gauging, at
most Minkowski ground states are possible. The existence of such Minkowski
ground states could be proven in the compact Abelian case.Comment: 30 pages, Latex, some references modified, typos in eq. (4.18) and
(5.3) corrected. Version to appear in Nuclear Physics
