Enabling users to move to different geographical locations within a network and still be able to maintain their connectivity and most essentially, continuity of service, is what makes any wireless network ubiquitous. Whilst challenging, modern day wireless networks, such as 3GPP-LTE, provision satisfactory mobility management (MM) performance. However, it is estimated that the number of mobile subscriptions will touch 9 billion and the amount of data traffic will expand by 10 times by 2021. To cope with such an exponential increase in cellular traffic and users alongside a burgeoning demand for higher Quality of Service (QoS), the 5G networks are expected to be highly dense and heterogeneous. This will severely challenge the existing MM solutions and ultimately render them ineffective as they will not be able to provide the required reliability, flexibility, and scalability. Consequently, to serve the 5G networks, a new perspective to MM is required. Hence, in this article we present a novel discussion of the functional requirements from MM strategies for 5G networks. We then provide a detailed assessment of whether the existing mechanisms conceived by standardization bodies such as IEEE, IETF, 3GPP (including the newly defined 5G standards) and ITU, and current research efforts meet these requirements. Next, in cognizance of these prior discussions, we present a study detailing the research challenges that exist in the design and implementation of MM strategies for 5G networks. Lastly, we chart out the potential 5G MM solutions and the associated capabilities they offer.