According to the invention, there is provided a novel soybean variety designated XB13T05. This invention thus relates to the seeds of soybean variety XB13T05, to the plants of soybean XB13T05 to plant parts of soybean variety XB13T05 and to methods for producing a soybean plant produced by crossing plants of the soybean variety XB13T05 with another soybean plant, using XB13T05 as either the male or the female parent.