In this work, we combine base station sleep mode strategies and device to device (D2D) communications to design solutions for 5G green mobile networks. The basic idea is that switching-off base stations allows to save energy while D2D technology guarantees coverage. We consider the realistic case of multi-layer cellular network and explore two sleep mode mechanisms: partial sleep mode (PSM) where only the frequency layer guaranteeing coverage at cell-edge is turned off, and deep sleep mode (DSM) where the base station is switched-off completely. Once a base station is switched-off multi-hop D2D communications are enabled to provide coverage. Cellular and D2D communications are modeled using queuing theory and sharing radio resources among them in an optimal way guaranteeing the stability of the system. We evaluate the time period of sleeping base stations in function of device battery discharging and hence the corresponding network energy savings. Results show that the combination of sleep mode strategies and D2D communications provides energy savings using an acceptable device battery discharge.