Impairments baseband model in-phase and quadrature-phase Imbalance (IQI) and Residual hardware impairments (RHI) are two key factors degrading the performance of wireless communication systems (WCSs), particularly when high-frequency bands are employed, as in 5G systems and beyond. The impact of either IQI or RHI on the performance of various WCSs has been investigated exclusively in a separate way. To fill this gap, in this paper, the joint effect of both IQI and RHI on the performance of a WCS subject to the sum of Fox's H-function fading model (SFHF) is investigated. Such a fading model generalizes most, if not all, of well-known fading and turbulence models. To this end, closed-form and asymptotic expressions for the outage probability (OP), channel capacity (CC) under constant power with optimum rate adaptation (ORA) policy, and average symbol error probability (ASEP) for both coherent and non-coherent modulation schemes. Specifically, all the analytical expressions are derived for three different scenarios: (i) ideal Tx and Rx impaired, (ii) Tx impaired and ideal Rx, and (iii) both Tx and Rx are impaired. Further, asymptotic expressions for OP, CC under ORA policy, and ASEP are obtained, based on which, insightful discussions on the IQI and RHI impacts are made. Alpha-mu and Malaga M turbulence with pointing error distribution models have been considered particular SFHF distribution cases. The analytical derivations, revealed by simulation results, demonstrate that the RF impairments' effects should be seriously taken into account in the design of next-generation wireless technologies.