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The paper presents a reinforcement learning solution to dynamic resource allocation for 5G radio access network slicing. Available communication resources (frequency-time blocks and transmit powers) and computational resources (processor usage) are allocated to stochastic arrivals of network slice requests. Each request arrives with priority (weight), throughput, computational resource, and latency (deadline) requirements, and if feasible, it is served with available communication and computational resources allocated over its requested duration. As each decision of resource allocation makes some of the resources temporarily unavailable for future, the myopic solution that can optimize only the current resource allocation becomes ineffective for network slicing. Therefore, a Q-learning solution is presented to maximize the network utility in terms of the total weight of granted network slicing requests over a time horizon subject to communication and computational constraints. Results show that reinforcement learning provides major improvements in the 5G network utility relative to myopic, random, and first come first served solutions. While reinforcement learning sustains scalable performance as the number of served users increases, it can also be effectively used to assign resources to network slices when 5G needs to share the spectrum with incumbent users that may dynamically occupy some of the frequency-time blocks.