Non-orthogonal multiple access (NOMA) has attracted much recent attention owing to its capability for improving the system spectral efficiency in wireless communications. Deploying NOMA in heterogeneous network can satisfy users' explosive data traffic requirements, and NOMA will likely play an important role in the fifth-generation (5G) mobile communication networks. However, NOMA brings new technical challenges on resource allocation due to the mutual cross-tier interference in heterogeneous networks. In this article, to study the tradeoff between data rate performance and energy consumption in NOMA, we examine the problem of energy-efficient user scheduling and power optimization in 5G NOMA heterogeneous networks. The energy-efficient user scheduling and power allocation schemes are introduced for the downlink 5G NOMA heterogeneous network for perfect and imperfect channel state information (CSI) respectively. Simulation results show that the resource allocation schemes can significantly increase the energy efficiency of 5G NOMA heterogeneous network for both cases of perfect CSI and imperfect CSI.