CCBYHandover (HO) is one of the key aspects of next-generation (NG) cellular communication networks that need to be properly managed since it poses multiple threats to quality-of-service (QoS) such as the reduction in the average throughput as well as service interruptions. With the introduction of new enablers for fifth-generation (5G) networks, such as millimetre wave (mm-wave) communications, network densification, Internet of things (IoT), etc., HO management is provisioned to be more challenging as the number of base stations (BSs) per unit area, and the number of connections has been dramatically rising. Considering the stringent requirements that have been newly released in the standards of 5G networks, the level of the challenge is multiplied. To this end, intelligent HO management schemes have been proposed and tested in the literature, paving the way for tackling these challenges more efficiently and effectively. In this survey, we aim at revealing the current status of cellular networks and discussing mobility and HO management in 5G alongside the general characteristics of 5G networks. We provide an extensive tutorial on HO management in 5G networks accompanied by a discussion on machine learning (ML) applications to HO management. A novel taxonomy in terms of the source of data to be utilized in training ML algorithms is produced, where two broad categories are considered; namely, visual data and network data. The state-of-the-art on ML-aided HO management in cellular networks under each category is extensively reviewed with the most recent studies, and the challenges, as well as future research directions, are detailed.