The design of an efficient radio access selection mechanism for 5G cellular networks is of paramount importance. Several proposals exist in the literature, but up to now the deployed systems are still using simple mechanisms mainly related to the evaluation of the RSS to make a handover decision. However, this is an inadequate solution for 5G networks. In this paper, we describe a novel multi-criteria handover scheme, we provide details on solutions for acquiring the necessary contextual information and we describe the algorithm to select the most appropriate RAT. Our solution is based on the use of fuzzy logic controllers for combining diverse inputs (such as a user's mobility, the load of the candidate base stations etc.) The efficiency of our mechanism is evaluated through appropriate simulations. The results related to throughput, delay and the number of the executed handovers clearly show the merits of our proposal when compared to a well-established LTE handover algorithm.