The gNodeB (gNB) in 5G-New Radio (5G-NR) is capable of beamforming and spatial multiplexing the users to achieve a multi-fold increase in the network capacity. With multiple active beams and the possibility of varying payload sizes, the resource allocation algorithm should optimally utilize the resources in time, frequency, and space. Otherwise, the multifold increase expected from the massive number of antennae will not be realized in practice. Further, in the 5G-NR downlink, each payload transmitted in the shared channel has an associated payload in the control channel. Thus, to have optimal resource utilization, the gNB should simultaneously consider the control and the shared channel payloads while allocating resources. Unlike the 4G-Long Term Evolution (4G-LTE), both control channel and shared channel support beamforming in 5G-NR. Hence, when the gNB uses the existing 4G-LTE algorithms for 5G-NR, they do not achieve the optimal resource allocation. Motivated by this, we propose a joint control and shared channel allocation for 5G-NR downlink that maximizes the sum-throughput while ensuring fairness in the allocation. We formulate this proposed resource allocation as an integer linear program. We also present low-complexity sub-optimal and approximation algorithms due to their practical usefulness. We then evaluate the proposed algorithms using system-level simulations and show that they significantly outperform the baseline algorithm. © 2021 IEEE.