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We study five-dimensional N=4 gauged supergravity coupled to five vector multiplets with compact and non-compact gauge groups U(1)×SU(2)×SU(2) and U(1)×SO(3,1). For U(1)×SU(2)×SU(2) gauge group, we identify N=4AdS5 vacua with U(1)×SU(2)×SU(2) and U(1)×SU(2)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 expectation values of dimension-two operators. In addition, we study AdS3×Σ2 geometries, for Σ2 being a two-sphere S2 or a two-dimensional hyperbolic space H2, dual to twisted compactifications of N=2 SCFTs with flavor symmetry SU(2). We find a number of AdS3×H2 solutions preserving eight supercharges for different twists from U(1)×U(1)×U(1) and U(1)×U(1)diag gauge fields. We numerically construct various RG flow solutions interpolating between N=4AdS5 critical points and these AdS3×H2 geometries in the IR. The solutions can also be interpreted as supersymmetric black strings in asymptotically AdS5 space. These types of holographic solutions are also studied in non-compact U(1)×SO(3,1) gauge group. In this case, only one N=4AdS5 vacuum exists, and we give an RG flow solution from this AdS5 to a singular geometry in the IR corresponding to an N=2 non-conformal field theory. An AdS3×H2 solution together with an RG flow between this vacuum and the N=4AdS5 are also given. [ABSTRACT FROM AUTHOR]