The generalized f(R) gravity with coupling in five-dimensional (SD) spacetime is studied on the basis of both the 4D generalized f(R) gravity with coupling and the pure f(R) gravity without coupling in 5D spacetime.Specifically,by assuming a hypersurface-orthogonal space-like Killing vector field in 5D spacetime,the generalization of the 4D generalized f(R) gravity to 5D can be realized,which can give the reduced 4-metric coupled with two scalar fields.In particular,we discuss a special class of models,i.e.,f1(R) =f2(R) =αRm (m ≠ 1),and choose B(Lm) =Lm =-ρ in the homogeneous and isotropic cosmology with the 4D Friedmann-Robertson-Walker metric.The numerical analysis shows that the parameter m can be constrained by means of the current observations for the deceleration parameter,which implies that this generalized f (R) model with coupling in 5D spacetime can account for the present accelerated expansion of the universe.