This paper examines network slicing within the radio access network which employs an orthogonal frequency division multiple access system for downlink communications. Its radio resources are allocated among slices configured for specific 5G use cases as well as other non-5G services. This work sets out to achieve optimal resource provisioning and power allocation within the context of priority slicing where slices are assigned priority levels by the base station. A mixed-integer non-linear programming problem is formulated to maximize the throughput of a best effort slice while satisfying the constraints of the high priority 5G slices. The problem is simplified and relaxed into a convex optimization problem. Three scenarios under various conditions are presented to serve as benchmarks. The impact of the chosen schedulers on the allocations, intra-slice, and inter-slice contentions is also examined. The results highlight that the wireless network can satisfy the quality-of-service requirements of opposing levels of priorities of traffic while simultaneously mitigating both inter-slice and intra-slice contentions under conditions mirroring that of practical wireless network deployments. Furthermore, it is proven that the convex approximation problem serves as a reasonable approximation of the original MINLP problem.