The emerging 5G communication network is gaining tremendous attention from mobile network operators, regulators, and academia due to the provisions of network densification, ultra-low latency and improved spectral and energy efficiencies. However, post-disaster EMS, which nowadays predominantly depends on the wireless communication infrastructure, is significantly lagging behind in terms of innovation, standards, and investments. Since the 5G vision is the revolution of the telecommunication industry, provisions of efficiently handling EMS is expected to be distributed, autonomous, and resilient to the network vulnerabilities due to both manmade and natural disasters. In this article, the 4G LTE approaches for typical post-disaster communication and their shortcomings will be discussed. We elaborate three typical post-disaster network scenarios when the network is congested, partly functional or completely isolated. The possible solution framework, for instance, Device-to-Device communication, drone-assisted communication, mobile ad hoc networks and Internet-of-Things, for post-disaster scenarios will be discussed. Given that spectrum allocation is critical for EMS, we assess the possible schemes for radio resource allocation specific for EMS in addition to the social responsibility of users in such critical situations.