With the advent of 5G mobile communication systems, the evolution of the Internet of Vehicles (IoV) will be greatly promoted, and it will be able to meet people's demands extremely in terms of performance and functional requirements. Moreover, fog computing has been proposed at the edge of the 5G-enabled IoV architecture, to provide data storage, calculation, and interaction with vehicles. Furthermore, the Global Navigation Satellite Systems (GNSS) play a significant role in future 5G-enabled IoV environment. However, navigation systems usually lose effectiveness because of various factors and disturbances in the 5G-enabled IoV, such as severe weather, GNSS device failure, and skyscrapers that block GNSS signals. Meanwhile, since some measurements come from the NLOS path, this can result in very large positioning errors. To address these challenges, this paper proposes a GNSS-free emergency location-based service (LBS) using fog computing in 5G-enabled IoV. Firstly, we propose the topology structure of the 5G-enabled IoV to address the problem of GNSS failure. Then, the operation procedures of emergency location service and the hierarchical logical architecture of the fog based service networks are designed. Finally, a vehicle positioning algorithm is proposed based on semi-definite programming (SDP) for positioning errors in the 5G-enabled IoV environment. Simulation results verify that the method can achieve high-precision location estimation for the 5G-enabled IoV.