The meaning of 5G is still a subject of discussion in the industry. However, the softwarization of networks is expected to shape the design, operation and management of 5G networks. The opportunity is then crucial for Telcos, vendors and IT players to consider the management of 5G networks during its design time and avoid the " build it first, manage it later " paradigm. However, network softwarization comes with its own set of challenges, including robustness, scalability and resilience. In this paper, we analyze the vulnerabilities of SDN (Software-Defined Networks) and NFV (Network Function Virtualization) from a fault management perspective, while taking into account the autonomic principles. In particular, we focus on resiliency and we propose a Self-Healing based framework for 5G networks to ensure services and resources availability.