This article presents a multi-intelligent reflecting surface (IRS)- and multi-unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) system for 5G/6G networks. In the studied system, multiple UAVs are integrated for providing services to large-scale user equipment (UEs) with the help of multiple IRSs. This article aims to minimize the overall cost including energy consumption, completion time, and maintenance cost of UAVs by jointly optimizing the trajectories of UAVs and phase shifts of IRSs. When solving this problem, one has to count in mind the deployment of stop points (SPs) of UAVs, and consider the association among UEs, and UAVs (i.e., which UE will send data to which UAV at which SP), the order of SPs, and the phase shifts of IRSs. Therefore, traditional optimization techniques may not solve the above-mentioned problem in an efficient way. To tackle the above-mentioned problem, this article proposes an algorithm called TPaPBA that consists of four phases. The first phase optimizes the SPs’ deployment via using a differential evolution algorithm having variable population size. As a result, all the SPs of UAVs can be obtained. Then, the second phase optimizes the association among UEs, SPs, and UAVs. Specifically, TPaPBA first adopts a clustering algorithm to optimize the SPs-UAVs association, and then a close criterion is introduced to optimize UEs-SPs association. Subsequently, third phase adopts a low-complexity greedy algorithm to optimize the order of SPs for UAVs. Finally, the phase shifts of IRSs are optimized to enhance the data rate between UEs and UAVs. The simulation results of TPaPBA on ten instances having UEs ranging from 100 to 1000, reveals that TPaPBA has significantly improved the system performance contribution and outperforms other approaches in terms of reducing the overall cost of UAVs.