Fifth generation (5G) wireless networks will target at energy and spectrum efficient solutions to cope with the increasing demands in capacity and energy efficiency. To achieve this joint goal, dense networks of small cells (SCs) are expected to overlay the existing macro cells. In parallel, for the SC connection to the core network, a promising solution lies in a mesh network of high capacity millimeter wave backhaul (BH) links. In the considered 5G architecture, each SC is able to forward its BH traffic to the core network through alternative paths, thus offering high BH network reliability. In this context, the joint problem of user association and BH routing becomes challenging. In this paper, we focus on this problem targeting at energy and spectrum efficient solutions. A low-complexity algorithm is proposed, which bases its user association and BH routing decision i) on minimizing the spectrum resources to guarantee the user rate, so as to provide high spectrum efficiency, and ii) on minimizing both the access network and BH route power consumption to provide high energy efficiency. Our results show that our solution provides better trade-offs between energy and spectrum efficiency than the state-of-the-art in 3GPP scenarios