GO:0052812:   phosphatidylinositol-3,4-bisphosphate 5-kinase activity
Catalysis of the reaction: 1-phosphatidyl-1D-myo-inositol 3,4-bisphosphate + ATP = a 1-phosphatidyl-1D-myo-inositol 3,4,5-trisphosphate + ADP + 2 H(+).