Catalysis of the reaction: a 1-phosphatidyl-1D-myo-inositol 3-phosphate + ATP = a 1-phosphatidyl-1D-myo-inositol 3,5-bisphosphate + ADP + H+.
ATP:1-phosphatidyl-1D-myo-inositol-3-phosphate 5-phosphotransferase activity