Towards the next generation networks, low earth orbit (LEO) satellites have been considered as a promising component for beyond 5G networks. In this paper, we study downlink LEO-5G communication systems in a practical scenario, where the integrated LEO-terrestrial system is over-loaded by serving a number of terminals with high-volume traffic requests. Our goal is to optimize resource scheduling such that the amount of undelivered data and the number of unserved terminals can be minimized. Due to the inherent hardness of the formulated quadratic integer programming problem, the optimal algorithm requires unaffordable complexity. To solve the problem, we propose a near-optimal algorithm based on alternating direction method of multipliers (ADMM-HEU), which saves computational time by taking advantage of the distributed ADMM structure, and a low-complexity heuristic algorithm (LC-HEU), which is based on estimation and greedy methods. The results demonstrate the near-optimality of ADMM-HEU and the computational efficiency of LC-HEU compared to the benchmarks.