Traffic safety and efficiency are extremely significant in both private and public transportation. The fifth-generation (5G)-enabled vehicular networks works wirelessly to share information among vehicles for helping drivers and passengers. Since the vehicle broadcasts the traffic status messages, privacy and security are considered as a challenging issue in 5G-enabled vehicular networks. In order to satisfy these privacy and security requirements, many privacy-preserving and security attacks schemes have been proposed. Nevertheless, since these schemes use a complex elliptic curve and bilinear pair cryptography operations, the performance efficiency of in terms of communication and computational costs is not satisfactory, which denial of service (DoS) attacks occurs. To address this, this paper proposes modular square root-based to resist denial of service (DoS) attacks (MSR-DoS) scheme in 5G-enabled vehicular networks. Our MSR-DoS scheme satisfies authenticity of source, integrity of message, pseudonym privacypreserving, unlinkable, traceable and revocable in vehicular networks. The security of our work is proved under burrows abadi needham (BAN) logic. The performance analysis and comparison shows that MSR-DoS scheme has less communication and computational costs as compared to the most recent existing works. Meanwhile, the proposed MSR-DoS scheme reduces the computation overhead of signing the message and verifying the message by 99.80% and 98.55%, respectively.