Catalyzes the oxygenation of arachidonic acid to 5-hydroperoxyicosatetraenoic acid (5-HPETE) followed by the dehydration of the hydroperoxide into an epoxide, 5,6- oxidoicosatetraenoic acid (LTA4), thereby participates in the first step in leukotriene biosynthesis and in the inflammatory processes. Also catalyzes the oxygenation of arachidonic acid into 8-hydroperoxyicosatetraenoic acid (8-HPETE) and 12-hydroperoxyicosatetraenoic acid (12-HPETE).