Heterogeneous network (HetNet) is an attractive solution for future cellular networks with high data rate and coverage requirements. In HetNets, small cells such as micro cells, pico cells, femto cells and relay node (RN) are added to the network of macro cells in the same region. A large number of low power RNs produces new cell edges with significant intra-cell and inter-cell interferences. In the uplink (UL) scenarios of timedivision based HetNets with RN, the user equipment (UE) desired signal may be interfered by the transmissions of the co-channel UEs during the first time slot and by the transmissions of the cochannel UEs or RNs during the second time slot. The interference caused by the RNs may significantly degrade the UE signal. UL transmission power control (PC) is essential for mitigating interference and, as a result, enhancing the cell edge and overall system performance. This research proposes a PC algorithm in order to mitigate the UL interference in 5g relay-based HetNets. This research also investigates the UL performance of HetNets when PC is applied at the RNs. Simulation results indicate that UL PC at the RNs greatly reduces average interference and improves average UL signal-to-interference-plus-noise ratio (SINR) and average UL end-to-end throughput compared to the situation in which UL PC is not implemented.