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We derive both BPS and non-BPS first-order flow equations for magneticallycharged black strings in five-dimensional N=2 abelian gauged supergravity,using the Hamilton-Jacobi formalism. This is first done for the coupling tovector multiplets only and U(1) Fayet-Iliopoulos (FI) gauging, and thengeneralized to the case where also hypermultiplets are present, and abeliansymmetries of the quaternionic hyperscalar target space are gauged. We then usethese results to derive the attractor equations for near-horizon geometries ofextremal black strings, and solve them explicitely for the case where theconstants appearing in the Chern-Simons term of the supergravity action satisfyan adjoint identity. This allows to compute in generality the central charge ofthe two-dimensional conformal field theory that describes the black strings inthe infrared, in terms of the magnetic charges, the CY intersection numbers andthe FI constants. Finally, we extend the r-map to gauged supergravity and useit to relate our flow equations to those in four dimensions.

Black string first order flow in N=2, d=5 abelian gauged supergravity