Multi-connectivity is a 5G key enabler to fulfill multi-service quality-of-service (QoS) requirements. This work examines an opportunistic resource allocation problem under multi-connectivity and limited backhaul capacity in evolved LTE using two utility functions: proportional fairness (PF) and utility proportional fairness (UPF). We then propose an efficient algorithm to deal with the formulated NP-hard problem. Such algorithm guarantees to produce a solution with an explicit bound on the optimal solution. Finally, simulation results justify that UPF utility function with opportunistic scheduling in multiconnectivity can better satisfy QoS requirements.