  We study five-dimensional $N=4$ gauged supergravity coupled to five vector
multiplets with compact and non-compact gauge groups $U(1)\times SU(2)\times
SU(2)$ and $U(1)\times SO(3,1)$. For $U(1)\times SU(2)\times SU(2)$ gauge
group, we identify $N=4$ $AdS_5$ vacua with $U(1)\times SU(2)\times SU(2)$ and
$U(1)\times SU(2)_{\textrm{diag}}$ symmetries and analytically construct the
corresponding holographic RG flow interpolating between these critical points.
The flow describes a deformation of the dual $N=2$ SCFT driven by vacuum
expaction values of dimension-two operators. In addition, we study $AdS_3\times
\Sigma_2$ geometries, for $\Sigma_2$ being a two-sphere $S^2$ or a
two-dimensional hyperbolic space $H^2$, dual to twisted compactifications of
$N=2$ SCFTs with flavor symmetry $SU(2)$. We find a number of $AdS_3\times H^2$
solutions preserving eight supercharges for different twists from $U(1)\times
U(1)\times U(1)$ and $U(1)\times U(1)_{\textrm{diag}}$ gauge fields. We
numerically construct various RG flow solutions interpolating between $N=4$
$AdS_5$ ciritcal points and these $AdS_3\times H^2$ geometries in the IR. The
solutions can also be interpreted as supersymmetric black strings in
asymptotically $AdS_5$ space. These types of holographic solutions are also
studied in non-compact $U(1)\times SO(3,1)$ gauge group. In this case, only one
$N=4$ $AdS_5$ vacuum exists, and we give an RG flow solution from this $AdS_5$
to a singular geometry in the IR corresponding to an $N=2$ non-conformal field
theory. An $AdS_3\times H^2$ solution together with an RG flow between this
vacuum and the $N=4$ $AdS_5$ are also given.
