For unforeseen natural disasters, such as earthquakes, hurricanes, and floods, etc., the traditional communication infrastructure is unavailable or seriously disrupted along with persistent secondary disasters. Under such circumstances, it is highly demanded to deploy emergency wireless communication (EWC) networks to restore connectivity in accident/incident areas. The emerging fifth-generation (5G)/beyond-5G (B5G) wireless communication system, like unmanned aerial vehicle (UAV) assisted networks and intelligent reflecting surface (IRS) based communication systems, are expected to be designed or re-farmed for supporting temporary high quality communications in post-disaster areas. However, the channel characteristics of post-disaster areas quickly change as the secondary disaster resulted topographical changes, imposing new but critical challenges for EWC networks. In this paper, we propose a novel heterogeneous $\mathcal{F}$ composite fading channel model for EWC networks which accurately models and characterizes the composite fading channel with reflectors, path-loss exponent, fading, and shadowing parameters in 5G-UAV based EWC networks. Based on the model, we develop the optimal power allocation scheme with the simple closed-form expression and the numerical results based optimal joint bandwidth-power allocation scheme. We derive the corresponding capacities and compare the energy efficiency between IRS and traditional relay based 5G-UAVs. Numerical results show that the new heterogeneous Fisher-Snedecor $\mathcal{F}$ composite fading channel adapted resource allocation schemes can achieve higher capacity and energy efficiency than those of traditional channel model adapted resource allocation schemes, thus providing better communications service for post-disaster areas.