Simultaneous wireless information and power transfer (SWIPT) technique offers a potential solution to ease the contradiction between high data rate and long standby time in the fifth generation (5G) mobile communication systems. In this paper, we focus on the SWIPT network design and optimization with 5G new frequencies. To design an efficient SWIPT network, we first investigate the propagation properties of 5G low-frequency (LF) and high-frequency (HF) channels. Specifically, a measurement campaign focusing on 3.5 GHz and 28 GHz is conducted in both outdoor and outdoor-to-indoor scenarios. Motivated by the measurement results, we design a dual-band SWIPT network, where the HF band is used for short-distance information delivery, while the LF band is used for short-distance energy transfer and long-distance information delivery. The designed network has a win-win architecture which can enhance the throughput of cell-edge users and improve the energy-harvesting efficiency of cell-center users. To further boost the network performance, we devise a joint power-and-channel allocation algorithm, which has the advantages of low complexity and fast convergence. Finally, simulation results demonstrate that the designed dual-band network outperforms the conventional single-band network in terms of energy-harvesting efficiency and user fairness, and the proposed algorithm can further upgrade the network performance significantly.