Recently, the concept of wake-up radio based access has been considered as an effective power saving mechanism for 5G mobile devices. In this article, the average power consumption of a wake-up radio enabled mobile device is analyzed and modeled by using a semi-Markov process. Building on this, a delay-constrained optimization problem is then formulated, to maximize the device energy-efficiency under given latency requirements, allowing the optimal parameters of the wake-up scheme to be obtained in closed form. The provided numerical results show that, for a given delay requirement, the proposed solution is able to reduce the power consumption by up to 40% compared with an optimized discontinuous reception (DRX) based reference scheme.