Due to the expectedly higher density of mobile devices and exhaust of radio resources, the fifth generation (5G) mobile networks introduce small cell concept in the radio access technologies, so-called Small Cell Networks (SCNs), to improve radio spectrum utilization. However, this increases the chance of handover due to smaller coverage of a micro base station, i.e., home eNodeB (HeNB) in 5G. Subsequently, the latency will increase as the costs of authenticated key exchange protocol, which ensures entity authentication and communication confidentiality for secure handover, also increase totally. Thus, this work presents a secure region-based handover scheme (ReHand) with user anonymity and fast revocation for SCNs in 5G. ReHand greatly reduces the communication costs when UEs roam between small cells within the region of a macro base station, i.e., eNB in 5G, and the computation costs due to the employment of symmetry-based cryptographic operations. Compared to the three elaborated related works, ReHand dramatically reduces the costs from 82.92% to 99.99%. Nevertheless, this work demonstrates the security of ReHand by theoretically formal proofs.