The innovative approach of “5G base stations + distributed renewable energy sources + repurposed electric vehicle batteries” utilizes the distributed renewable energy. This not only facilitates the cascading utilization of retired electric vehicle batteries but also promotes the low-carbon development of communication infrastructure. However, the uncertainty of distributed renewable energy and communication loads poses challenges to the safe operation of 5G base stations and the power grid. Therefore, this paper proposes a two-stage robust optimization (TSRO) model for 5G base stations, considering the scheduling potential of backup energy storage. At the day-ahead stage, the objective function is to minimize the comprehensive operational cost. During the intraday stage, based on day-ahead predicted data of renewable energy output and load and errors, the model adjusts the backup energy storage of the 5G base station and the electricity exchanged with the power grid. This adjustment aims to minimize the scheduling cost. Then, by assessing the dispatchable capacity of the base station's backup energy storage and integrating it as a boundary constraint into the optimization model. The nest column-and-constraint generation (N-CCG) algorithm is employed to obtain the purchase and sale power and charge-discharge power, thereby enhancing the reliability of base station power supply. Simulation results indicate that the method proposed in this paper, enables the base station operation to account for more uncertainties and promotes the effective utilization of renewable energy.