Vehicular networks are known for their dynamic topology, high mobility, and frequent disconnections. Unmanned aerial vehicles (UAVs) have been recently used as instant communication relays to bridge the communication gaps between terrestrial vehicles to improve connectivity in vehicular networks and overcome the aforementioned problems. Despite the existing work in the literature where each vehicle connects directly to UAVs, this work studies how clustering and different densities of vehicles affect delay and energy efficiency in a UAV-based vehicular network integrated with 5G technology. Consequently, this work addresses the problem of UAV enabling vehicular ad-hoc networks (VANETs) in a highway scenario, where UAVs serve as an effective complement to forward data packets between vehicles in the absence of sufficient fixed infrastructures in an emergency situation. The main objective of this work is to minimize the delay while maximizing the energy efficiency by minimizing the power consumption and maximizing the total data rate under realistic conditions, while nonorthogonal multiple access (NOMA) is also adopted as an alternative answer for the effective utilization of limited bandwidth. The free-flowing traffic follows a Poisson stochastic process where each vehicle is assigned a random speed selected from a truncated Gaussian distribution. To this end, a novel modification of fast global -means is adopted to partition vehicles, allowing communication between clusters by vehicle-to-vehicle links, while data packets between clusters are relayed through UAVs. By computing the convex approximation of the objective function and the constraints, the original problem with the mixed-integer, nonconvex, and nonlinear form is solved by the proposed iterative inner penalty function algorithm. Finally, extensive simulations are conducted to validate the superiority of the proposed method in terms of various metrics. The results indicate that the relaying task in the proposed UAV-assisted VANET based on 5G technology is perfectly suited to enhance the network connectivity.