In this paper, we propose a non-orthogonal random access (NORA) technique for the uplink 5G networks, in which user equipments (UEs) make use of the channel inversion so that their received power at the base station (BS) can satisfy a certain threshold condition. In particular, each UE opportunistically adjusts its transmit power according to its channel gain. We also mathematically analyze the system throughput and energy efficiency (EE) of the proposed NORA. Finally, we show the performance of the proposed NORA technique through extensive computer simulations.