Catalyzes the conversion of L-ornithine to N(5)-hydroxyornithine, the first step in the biosynthesis of all hydroxamate-containing siderophores, such as pyoverdin. Pyoverdin is a hydroxamate siderophore composed of a 6,7-dihydroxyquinoline-containing fluorescent chromophore joined to the N-terminus of a partly cyclic octapeptide (D-Ser-L-Arg-D-Ser-L-N(5)-OH-Orn-L-Lys-L-N(5)-OH-Orn-L-Thr-L-Thr in strain PAO1). Specific for NADPH, which plays a role in stabilization of the C4a-hydroperoxyflavin intermediate. L-ornithine + NADPH + O2 = H2O + N(5)-hydroxy-L-ornithine + NADP(+) Binds 1 FAD per subunit. Optimum pH is 8.0-8.5. Siderophore biosynthesis; pyoverdin biosynthesis. Homotetramer. Belongs to the lysine N(6)-hydroxylase/L-ornithine N(5)-oxygenase family.