The emerge of fifth-generation (5G) wireless networks has started a new era of the development of wireless mobile networks. Security of the 5G wireless networks is the major concern when they are deployed for commercial applications. The third-generation partnership project (3GPP) has specified security functionality of 5G wireless in its standard release 16. However, it is prone to different attacks such as Denial of Service (DoS) attacks and false base-station attacks. Particularly, secure handover becomes a critical issue in the operation of the 5G mobile networks. In the paper, we propose an efficient and secure handover authentication protocol using the Chinese remainder theory at neighbor base stations, gNodeBs (gNBs) for secure handovers. The security of the proposal is formally evaluated to demonstrate its ability against various malicious attacks. The performance of the proposed scheme in terms of the delay incurred and energy consumption is evaluated by using JAVA simulation. The results obtained show that our scheme is secure and efficient with a relatively low energy consumption, which is suitable for devices in high-speed movements.