The 5G-enabled vehicular network is an innovative technology that has promise for intelligent transportation systems. It enables the transmitting of messages about traffic that deliver the most recent information on congestion, road conditions, and driving surroundings. The communication channel used by vehicle networks is inherently open, which unfortunately exposes the system to privacy and security concerns. To solve the problems of deploying a safe vehicular network, some academics have put forth plans. However, a number of current methods have significant computational or communication overhead costs. To solve this problem, an efficient and secure authentication with a privacypreserving (ES-APP) scheme established elliptic curve encryption is introduced. With the proposed ES-APP, the data signed and verified for vehicle-to-vehicle and vehicle-to-infrastructure modes in the 5G-based vehicular network are more effective. The ES-APP scheme’s goal is to meet the criteria for the security and privacy of the 5G-enabled automotive network. Ultimately, this work discusses the critical survey of the existing studies and the expected outcome for the ESAPP scheme and further works in the 5G-enabled vehicular network.