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Using a cache to improve efficiency and to save on the cost of a computer system has been a field that attracts many researchers, including those in the area of cellular network systems. The first part of this chapter focuses on adaptive cache management schemes for cloud radio access networks (CRAN) and multi-access edge computing (MEC) of 5G mobile technologies. Experimental results run through CloudSim show that the proposed adaptive algorithms are effective in increasing cache hit rate, guaranteeing QoS, and in reducing algorithm execution time. In second part of this chapter, a new cache management algorithm using Zipf distribution to address dynamic input is proposed for CRAN and MEC models. A performance test is also run using iFogSim to show the improvement made by the proposed algorithm over the original versions. This work contributes in the support of 5G for IoT by enhancing CRAN and MEC performance; it also contributes to how novel caching algorithms can resolve the unbalanced input load caused by changing distributions of the input traffic.