<p>The 5G network enables various innovative applications and encompasses three primary services: ultra-reliable low-latency communication, massive machine-type communication, and enhanced mobile broadband. Network slicing serves as a fundamental component of 5G networks. The 5G Cloud Radio Access Network (C-RAN) employs a network-slicing framework to define distinct virtual networks that cater to standard use cases across a shared physical network. The 5G CRAN faces constraints in radio resources while managing a surge in data traffic volume, necessitating efficient resource allocation systems to ensure the Quality of Service for Slices. This study introduces a system for adaptive slice allocation in the 5G C-RAN, where the priority of slices is adjusted in real-time based on the prevailing network conditions. We propose a second system, which is a delay-aware ASA (DA-ASA) system. This system introduces a maximum time delay tolerance to Adaptive Slice Allocation (ASA), serving as an additional parameter in the calculations of dynamic priority. The proposed system has been expanded to consider the tolerances for traffic delays. The ASA system implements dynamic resource allocation and slice admission control to enhance resource utilization within the network while ensuring that the quality of service requirements of each Slice are upheld. Moreover, we evaluate the total blocking probability, average waiting time, and resource utilization of the ASA system through simulation experiments. We also compare the proposed system with the Static Slice Allocation (SSA) system, a modified version of an existing scheme. The findings indicate that the DA-ASA and ASA systems surpass the SSA system by attaining a superior balance of system utilization, slice isolation, and QoS provision.</p>