New 5G architecture gives access to New Radio (NR) with co-exist LTE. 3GPP LTE-A transition towards NR is a wireless technology that is widely employed in the cellular mobile network to support significantly high volume traffic. In this paper, we propose the best N-subset reduction and a modified RME algorithm (BNSRME) as an uplink multiuser scheduler. It is responsible for allocating resources among the active users in the most effective manner. The N-subset reduction method selects the best chunk of continuous resource blocks from the available system bandwidth. Users are assigned chunks based on channel-dependent selection and utility function. The BNSRME scheduling algorithm aims to optimize performance, spectral efficiency, and allows multiuser scheduling where multiple active users are allocated the same time-frequency resources. We consider the threshold cap SNRT to improve sensitivity quality for satisfactory users. The approach is MU scheduling which will be the most commonly deployed in non-stand-alone (NSA) 5G uplink cellular network. The result shows that the system spectral efficiency improves by 32.55 % by using the proposed multiuser algorithm compared to single user scheduling in an uplink. It has been shown that its performance can be further improved by using the MU-MIMO system.