One of the most notable challenges in wireless communications is energy scarcity, which has attracted considerable attention in Fifth Generation (5G) wireless network research. This paper investigates the performance of energy harvesting (EH) relays under the best relay selection (BRS) scheme. The results show degradation of spectral efficiency (SE) due to EH relaying compared with conventional cooperative relaying (CR). Conversely, EH relaying provides a positive gain compared with conventional CR, increasing the lifetime of the network and decreasing energy consumption (EC) and operational cost. Moreover, the EH relaying network has better energy efficiency (EE) compared with conventional relaying networks. Results show that when EH relaying is applied, EE is improved through an increased number of relays. Finally, the SE-EE metric is presented for both conventional and EH relays. Results show that the performance of the proposed technique was able to achieve a maximum SE of 1.4 bits/s/Hz and maximum EE at 0.6 bits/s/Hz, and for the case of conventional relays, a maximum SE of 2 bits/s/Hz and EE at 1.1 bits/s/Hz. This result implies that the proposed EH scheme provides an optimum solution for energy-constrained wireless CR systems.