The problem of joint power and admission control (JPAC) is a critical issue encountered in underlay cognitive radio networks (CRNs). Moving forward towards the realization of Fifth Generation (5G) and beyond, where optimization is envisioned to take place in multiple performance dimensions, it is crucially desirable to achieve high sum throughput with low power consumption. In this work, a multi-objective JPAC optimization problem that jointly maximizes the sum throughput and minimizes power consumption in underlay CRNs is formulated. An enhanced swarm intelligence algorithm has been developed by hybridizing two new enhanced Particle Swarm Optimization (PSO) variants, namely two-phase PSO (TPPSO) and diversity global position binary PSO (DGP-BPSO) variants employed to optimize the multi-objective JPAC problem. The performance of the enhanced swarm intelligence algorithm in terms of convergence speed and stability, while optimizing both the sum throughput and power consumption, is investigated under three different operational scenarios defined by their single objective priorities, which translate to sum throughput and power consumption preferences. Simulation results have proven the effectiveness of the enhanced swarm intelligence algorithm in achieving high sum throughput and low power consumption under the three operational scenarios when the network includes an arbitrary number of primary and secondary users. Comparing the hybrid SPSO approach and the proposed approach, the proposed scheme has shown its effectiveness in increasing the sum throughput to 7%, 16%, and 31% under the multimedia, balanced and power saving operational scenarios, respectively. In addition, the proposed approach is more power efficient as it can provide additional power savings of 3.58 W, 2.48 W, and 1.6741 W under the aforementioned operational scenarios, respectively.