Catalyzes the phosphorylation of phosphatidylinositol 5-phosphate (PtdIns5P) on the fourth hydroxyl of the myo-inositol ring, to form phosphatidylinositol 4,5-bisphosphate (PtdIns(4,5)P2). Has both ATP- and GTP-dependent kinase activities. a 1,2-diacyl-sn-glycero-3-phospho-(1D-myo-inositol-5-phosphate) + ATP = a 1,2-diacyl-sn-glycero-3-phospho-(1D-myo-inositol-4,5-bisphosphate) + ADP + H(+) 1,2-dihexadecanoyl-sn-glycero-3-phospho-(1D-myo-inositol-5-phosphate) + ATP = 1,2-dihexadecanoyl-sn-glycero-3-phospho-(1D-myo-inositol-4,5-bisphosphate) + ADP + H(+) 1,2-dihexadecanoyl-sn-glycero-3-phospho-(1D-myo-inositol-5-phosphate) + GTP = 1,2-dihexadecanoyl-sn-glycero-3-phospho-(1D-myo-inositol-4,5-bisphosphate) + GDP + H(+) In rod outer segments, activated by light. Homodimer. Phosphorylated in tyrosines. Phosphorylation is induced by light and increases kinase activity.