To achieve "carbon peaking" and "carbon neutralization", the access of large-scale 5G communication base stations brings new challenges to the optimal operation of new power systems, but also provides new opportunities for the low-carbon development of distribution networks. This paper develops a method to consider the multi-objective cooperative optimization operation of 5G communication base stations and active distribution network (ADN), constructs a description model for the operational flexibility of 5G communication base station. Based on this, a multi-objective cooperative optimization 5G communication base station operating model and active distribution network considering the system operation economy and minimum carbon emissions as the optimization objectives are established. In the above model, by encouraging 5G communication base stations to engage in demand response (DR), the renewable energy sources (RES) and 5G communication base stations in ADN are concurrently scheduled, and the uncertainty of RES and communication load is described by using interval optimization method. Finally, the problem is solved by combining the equivalent transformation based on interval analysis and the non dominated sorting genetic algorithm. The analysis results of the example show that participation in grid side dispatching through the flexible response capability of 5G communication base stations can enhance the power system's renewable energy consumption and usage efficiency, resulting in significant low-carbon benefits.