GO:0000285:   1-phosphatidylinositol-3-phosphate 5-kinase activity
Catalysis of the reaction: a 1-phosphatidyl-1D-myo-inositol 3-phosphate + ATP = a 1-phosphatidyl-1D-myo-inositol 3,5-bisphosphate + ADP + 2 H(+).