In the past few years, the industry and academia have been working hard to establish and standardise vehicle-to-everything (V2X) communications, which is one of the vital emerging services for next generation wireless networks. Therewith, to control radio resource properly with balanced implementation complexity, a full-duplex V2V discovery mechanism in a 5G-V2X network based on a random backoff procedure is proposed to better utilize radio resources on which nearby vehicles establish their links. The main aims are to reduce complexity, latency, improve throughput and guarantee stability for V2V communication. The unemployed cellular network channel operates in full-duplex mode and leaves the channel as soon as they are informed that someone is in place through latency and throughput analysis technique. The channel sensing and identification are done in a cooperative manner before transmission. Furthermore, two effective resource distribution algorithms are proposed that grant the optimum resource distribution for V2V and V2I-Users. The detection and the throughput of full-duplex V2V communication in the proposed scheme have been formulated and the performance of the proposed scheme and validity of corresponding analysis are verified through simulation experiments.