The incoming era of the Fifth Generation (5G) Fog Computing (FC)-supported Radio Access Networks (shortly, 5G FOGRANs) aims at exploiting the virtualization of the computing/networking resources. The goal is to allow battery-powered wireless devices to augment their limited native resources through the seamless (e.g., live) migration of Virtual Machines (VMs) towards nearby Fog data centers. For this purpose, the bandwidths of the multiple heterogeneous Wireless Network Interface Cards (WNICs) typically equipping the current wireless devices may be used in parallel under the control of the emerging MultiPathTCP (MPTCP) protocol. However, due to the fading and mobility-induced phenomena impairing the underlying RANs, the energy consumptions and migration delays of the current state-of-the-art VM migration techniques may drastically reduce their expected benefits. Motivated by these considerations, in this paper, we analytically characterize, implement in software and numerically test the optimal minimum-energy Settable-Complexity Bandwidth Manager (SCBM) for the live migration of VMs over MPTCP-supported 5G FOGRAN connections. The key features of the proposed SCBM are that: (i) its implementation complexity is settable on-line, in order to attain the targeted energy consumption-vs.-implementation complexity tradeoff; (ii) it minimizes the energy consumed by the migration process under hard QoS constraints on the allowed migration time and downtime;and, (iii) by leveraging a suitably designed adaptive mechanism, it is capable to quickly react to (possibly, unpredicted) fading and/or mobility-induced abrupt changes of the operating conditions without requiring and forecasting support. We numerically test and compare the energy and delay performances of the proposed adaptive SCBM under several 3G/4G/WiFi FOGRAN scenarios by considering a number of synthetic and real-world workloads. The obtained numerical results point out that: (i) the energy savings of the proposed adaptive SCBM over the benchmark one currently implemented by legacy Xen, KWM and VMware hypervisors are typically over 25% and approach 70% when the migrated applications are memory-write intensive; and, (ii) the MPTCP may reduce the energy consumption of the proposed SCBM over legacy SinglePathTCP (SPTCP) more than 50% under strict real-time limits on the allowed migration times.