Catalyzes the introduction of a cis-double bond at the delta(5) position of existing saturated fatty acids attached to membrane phospholipids. It is not strictly specific for palmitic acid (C16) but can also accept C14 as well as C18 species to yield unsaturated fatty acids. Lipid metabolism; fatty acid metabolism. Transcriptionally regulated by DesR/DesK in response to cold shock. Belongs to the fatty acid desaturase type 1 family.