Unmanned aerial vehicles (UAVs) extend 5G network coverage by acting as mobile relays or onboard base stations (BSs) to connect with cellular BSs and user equipments (UEs). Their high mobility causes frequent Internet Protocol (IP) handoffs, affecting the quality of service (QoS) for connected devices. The 5G core network has improved with separate control and data planes, along with software-defined enhancements for better handoff management. However, centralized mobility management (CMM) still faces challenges like non-optimized routing and performance issues, especially in scenarios, like, UAV-assisted vehicular communication in smart cities and UAV-assisted remote construction and mining site. Distributed mobility management (DMM) is a promising alternative that decentralizes control plane anchors, improving scalability and efficiency. Existing DMM solutions, such as D-MIPv6, D-PMIPv6, D-SDN, and D-Routing, still require significant adaptation for seamless integration into UAV-assisted 5G networks. This paper integrates standard DMM schemes into UAV-based 5G networks, evaluates and analyses their performance across different UAV-assisted scenarios. Our findings indicate that for higher vehicular node velocity, longer pause times, lower handoff probability, and lower wireless link failure probability, U-SDN-DMM and U-D-Routing (UAV versions of SDN-DMM and D-Routing) perform best. However, in other conditions, these schemes become inefficient due to their high signaling costs.