Has kinase activity and phosphorylates inositol-1,3,4,5,6-pentakisphosphate (Ins(1,3,4,5,6)P5) to produce 1,2,3,4,5,6-hexakisphosphate (InsP6), also known as phytate. 1D-myo-inositol 1,3,4,5,6-pentakisphosphate + ATP = 1D-myo-inositol hexakisphosphate + ADP + H(+) The EXKPK motif is conserved in inositol-pentakisphosphate 2-kinases of both family 1 and 2. Belongs to the IPK1 type 1 family.