Abstract From five-dimensional N = 4 matter-coupled gauged supergravity, smooth time-dependent cosmological solutions, connecting a dS 5−d × H d (with d = 2, 3) spacetime at early times to a dS 5 spacetime at late times, are presented. The solutions are derived from the second-order equations of motion arising from all the gauged theories that can admit dS 5 solutions. There are eight such theories constructed from gauge groups of the form SO(1, 1) × G nc and SO ( 1 , 1 ) diag ( n ) × G nc , with n = 2, 3, where G nc is a non-compact gauge factor whose compact part must be embedded entirely in the matter symmetry group of 5D matter-coupled supergravity. Furthermore, we analyze how the cosmological solutions and their corresponding dS 5 vacua cannot arise from the first-order equations that solve the second-order field equations.