Device-to-device (D2D) connectivity is likely to represent a major enabling technology for future fifth generation (5G) radio access networks. In this paper, we introduce a new model for device cooperation in 5G radio access networks termed frequency-selective soft forwarding (FSSF). FSSF is based on soft-combining by a target user equipment (TUE) of selectively forwarded soft information data by a set of cooperating user equipments (CUEs) acting as mobile relays towards the TUE. FSSF exploits the inherent frequency selectivity and broadcast nature of the downlink radio access channel for the sake of enabling efficient device cooperation and seamless integration of D2D connectivity into cellular radio access networks. Several variants of FSSF are investigated, including centralized and distributed approaches, thus offering various tradeoffs of performance versus signaling overhead cost. Exhaustive simulation results using a state-of-the-art long-term evolution (LTE)-compliant link-level simulator show that FSSF well outperforms baseline device cooperation schemes relying on conventional decode-and-forward (DF) relaying and approaches the performance of optimal joint reception with significantly lower cost in terms of D2D resource utilization and signaling overhead.