Auto-scaling techniques aim to keep the right number of active servers for the current load: if this number is too small we risk service disruption, but if it is too large we waste resources. Despite the interest in the efficient operation of this type of systems, no prior work has addressed auto-scaling techniques for Network Function Virtualization (NFV) with stringent reliability requirements such as those envisioned in 5G (5 or 6 nines). To achieve such levels of reliability, we need to account for both the activation delay until servers become available (i.e., the wake-up or activation time) and the fallible nature of servers (which may fail with some probability). In this article, we build on control theory to design an auto-scaling technique for a server farm for NFV that guarantees certain reliability while minimizing the number of active resources. We show that the use of well-established tools from control theory results in convergence times much shorter than those obtained with state-of-the-art reinforcement learning techniques. This shows that, despite the current trend to apply machine learning to all sorts of networking problems, there may be some cases where other techniques (such as control theory) can be more suitable.