The 5G mobile communication network provides seamless communications between users and service providers and promises to achieve several stringent requirements, such as seamless mobility and massive connectivity. Although 5G can offer numerous benefits, security and privacy issues still need to be addressed. For example, the inclusion of small cell networks (SCN) into 5G brings the network closer to the connected users, providing a better quality of services (QoS), resulting in a significant increase in the number of Handover procedures (HO), which will affect the security, latency and efficiency of the network. It is then crucial to design a scheme that supports seamless handovers through secure authentication to avoid the consequences of SCN. To address this issue, this article proposes a secure region-based handover scheme with user anonymity and an efficient revocation mechanism that supports seamless connectivity for SCNs in 5G. In this context, we introduce three privacy-preserving authentication protocols, i.e., initial authentication protocol, intra-region handover protocol and inter-region handover protocol, for dealing with three communication scenarios. To the best of our knowledge, this is the first paper to consider the privacy and security in both the intra-region and inter-region handover scenarios in 5G communication. Detailed security and performance analysis of our proposed scheme is presented to show that it is resilient against many security threats, is cost-effective in computation and provides an efficient solution for the 5G enabled mobile communication.