This paper proposes an Edge-Enhanced Metro FiWi strategy to meet the increasing requirements of connectivity, reliability and latency for various Internet of Things applications in 5G era. Based on the fiber-wireless (FiWi) network, the networks architecture considered in this paper contains the metro network and access network facilitated by global control and management. The deployment of 5G makes energy consumption a severe issue, especially in access networks. Edge-Enhanced Metro FiWi with expanded coverage and intensive device deployment consumes even more energy, making the design of energy conservation mechanisms inevitable. Different from traditional energy-saving methods of optical network units (ONU) and mesh access points that control devices independently based on their own load conditions, this paper considers the joint optimization of sleep nodes across the network based on network states via matching game theory. A load adaptive energy-saving strategy is proposed to dynamically determine the optimal number of sleeping devices according to the network traffic. Considering the influence of route selection on sleeping node selection, our routing policy aggregates the traffic to the least number of destination nodes to set free as many ONUs as possible. Finally, a two-level many-to-one two-sided matching game model that maximizes the profit of each participant is adopted to solve the energy consumption minimization problem within delay constraints. The simulation results show that compared with threshold-based sleep mode and the shortest path first routing algorithm, the proposed strategy significantly reduces the energy consumption and keeps the delay under control.