The fifth generation (5G) system is the forthcoming generation of the mobile communication system. It has numerous additional features and offers an extensively high data rate, more capacity, and low latency. However, these features and applications have many problems and issues in terms of security, which has become a great challenge in the telecommunication industry. This paper aimed to propose a solution to preserve the user identity privacy in the 5G system that can identify permanent identity by using Variable Mobile Subscriber Identity, which randomly changes and does not use the permanent identity between the user equipment and home network. Through this mechanism, the user identity privacy would be secured and hidden. Moreover, it improves the synchronization between mobile users and home networks. Additionally, its compliance with the Authentication and Key Agreement (AKA) structure was adopted in the previous generations. It can be deployed efficiently in the preceding generations because the current architecture imposes minimal modifications on the network parties without changes in the authentication vector's message size. Moreover, the addition of any hardware to the AKA carries minor adjustments on the network parties. In this paper, the ProVerif is used to verify the proposed scheme.