The 5G network is designed to serve three main use cases: enhanced mobile broadband (eMBB), massive machine-type communications (mMTC), and ultra-reliable and low-latency communications (uRLLC). There are many new technological enablers, including the cloud radio access network (C-RAN) and network slicing, that can support 5G and meet its requirements. The C-RAN combines both network virtualization and based band unit (BBU) centralization. Using the network slicing concept, the C-RAN BBU pool can be virtually sliced into three different slices. 5G slices require a number of Quality of service (QoS) metrics, such as average response time and resource utilization. In order to enhance the C-RAN BBUs utilization while protecting the minimum QoS of the coexisting three slices, a priority-based resource allocation with queuing model is proposed. The uRLLC is given the highest priority, while eMBB has a higher priority than mMTC services. The proposed model allows the eMBB and mMTC to be queued and the interrupted mMTC to be restored in its queue to increase its chance to reattempt the service later. The proposed model’s performance measures are defined and derived using a continuous-time Markov chain (CTMC) model and evaluated and compared using different methodologies. Based on the results, the proposed scheme can increase C-RAN resource utilization without degrading the QoS of the highest-priority uRLLC slice. Additionally, it can reduce the forced termination priority of the interrupted mMTC slice by allowing it to re-join its queue. Therefore, the comparison of the results shows that the proposed scheme outperforms the other states of the art in terms of improving the C-RAN utilization and enhancing the QoS of eMBB and mMTC slices without degrading the QoS of the highest priority use case.