This paper proposes an intensive study for common-mode voltage (CMV) elimination/reduction in a five-level dual T-type multilevel converter (5LDT-MLC) drive. An advanced and fast model predictive control (MPC) approach is developed for CMV reduction (CMVR) and CMV elimination (CMVE) based on preselection of the switching states (SS). In addition, the proposed approach considers the torque control and the capacitor balancing of the proposed drive as essential aspects of MLC drives. A detailed study for the impact of the converter SS on the CMV is presented. The main features of the proposed MPC approach are reducing the complexity of the cost-function, the tuning burden of the weighting factors, and the computation time by more than 80% compared to conventional MPC techniques. A hardware implementation based on Silicon Carbide (SiC) T-type MLC is built. The experimental results demonstrate the effectiveness of the proposed MPC approach to mitigate/eliminate the CMV along with achieving the torque command and balancing the DC link capacitors. Unlike conventional CMVR techniques, the proposed approach reduces the CMV by 75% of its normal values without jeopardizing the harmonic contents, drive efficiency, and flux as well as torque ripples.