Next generation mobile networks are expected to integrate multiple drones organized in Flying Ad Hoc Networks (FANETs) to support demanding and diverse services. The highly mobile drones should always be connected to the network in order to satisfy the strict requirements of upcoming applications. As the number of drones increases, they burden the network with the management of signaling and continuous monitoring of the drones during data transmission. Therefore, designing transmission mechanisms for fifth-generation (5G) drone-aided networks and using clustering algorithms for their grouping is of paramount importance. In this paper, a clustering and selection algorithm of the cluster head is proposed together with an efficient Group Handover (GHO) scheme that details how the respective Point of Access (PoA) groups will be clustered. Subsequently, for each cluster, the PoA elects a Cluster Head (CH), which is responsible for manipulating the mobility of the cluster by orchestrating the handover initiation (HO initiation), the network selection, and the handover execution (HO execution) processes. Moreover, the members of the cluster are informed about the impending HO from the CH. As a result, they establish new uplink and downlink communication channels to exchange data packets. In order to evaluate the proposed HO scheme, extensive simulations are carried out for a next-generation drone network architecture that supports Internet of Things (IoT) and multimedia services. This architecture relies on IEEE 802.11p Wireless Access for Vehicular Environment (WAVE) Road Side Units (RSUs) as well as Long-Term Evolution Advanced (LTE-A) and IEEE 802.16 Worldwide Interoperability for Microwave Access (WiMAX). Furthermore, the proposed scheme is also evaluated in a real-world scenario using a testbed deployed in a controlled laboratory environment. Both simulation and real-world experimental results verify that the proposed scheme outperforms existing HO algorithms.