The high data traffic requirements of the new generation 5G networks will be satisfied with effective and efficient mobility and handover management. However, dense or ultra-dense small cell (eNB) placements in 5G networks may lead to some problems, such as latency, handover failures, frequent handover, ping-pong effect, etc. In this study, we proposed an Entropy-based simple additive weighting decision-making method for multi-criteria handover in software-defined networking (SDN) based 5G small cells for the solution of the aforementioned problems. This method provides the connection of the mobile node to the most suitable eNB using bandwidth, user density and SINR parameters. The proposed handover method is compared with conventional LTE handover and distributed approach in terms of delay, block ratio, handover failure and throughput according to the varying number of mobile users. The scalability of handovers for both approaches according to the user number are also analysed. According to the simulation results, the proposed approach achieved 15%, 48% and 22% improvement in handover delay, blocking probability and throughput, respectively, compared to the conventional LTE handover.