With increasing focus on Artificial Intelligence (AI) applications, Deep Neural Networks (DNNs) have been successfully used in a number of application areas. As the number of layers and neurons in DNNs increases rapidly, significant computational resources are needed to execute a learned DNN model. This ever-increasing resource demand of DNNs is currently met by large-scale data centers with state-of-the-art GPUs. However, increasing availability of mobile edge computing and 5G technologies provide new possibilities for DNN-driven AI applications, especially where these application make use of data sets that are distributed in different locations. One fundamental process of a DNN-driven application in mobile edge clouds is the adoption of “inferencing” - the process of executing a pre-trained DNN based on newly generated image and video data from mobile devices. We investigate offloading DNN inference requests in a 5G-enabled mobile edge cloud (MEC), with the aim to admit as many inference requests as possible. We propose exact and approximate solutions to the problem of inference offloading in MECs. We also consider dynamic task offloading for inference requests, and devise an online algorithm that can be adapted in real time. The proposed algorithms are evaluated through large-scale simulations and using a real world test-bed implementation. The experimental results demonstrate that the empirical performance of the proposed algorithms outperform their theoretical counterparts and other similar heuristics reported in literature.