Multicasting is a key feature of cellular systems, which provides an efficient way to simultaneously disseminate a large amount of traffic to multiple subscribers. However, the efficient use of multicast services in fifth-generation (5G) New Radio (NR) is complicated by several factors, including inherent base station (BS) antenna directivity as well as the exploitation of antenna arrays capable of creating multiple beams concurrently. In this work, we first demonstrate that the problem of efficient multicasting in 5G NR systems can be formalized as a special case of multi-period variable cost and size bin packing problem (BPP). However, the problem is known to be NP-hard, and the solution time is practically unacceptable for large multicast group sizes. To this aim, we further develop and test several machine learning alternatives to address this issue. The numerical analysis shows that there is a trade-off between accuracy and computational complexity for multicast grouping when using decision tree-based algorithms. A higher number of splits offers better performance at the cost of an increased computational time. We also show that the nature of the cell coverage brings three possible solutions to the multicast grouping problem: (i) small-range radii are characterized by a single multicast subgroup with wide beamwidth, (ii) middle-range deployments have to be solved by employing the proposed algorithms, and (iii) BS at long-range radii sweeps narrow unicast beams to serve multicast users.