Catalysis of the reaction: NAD(P)+ + (15S)-15-hydroxy-5,8,11-cis-13-trans-icosatetraenoate = NAD(P)H + H+ + 15-oxo-5,8,11-cis-13-trans-icosatetraenoate.
15-hydroxyeicosatetraenoate dehydrogenase activity