Contributes to tetrahydrofolate metabolism. Helps regulate carbon flow through the folate-dependent one-carbon metabolic network that supplies carbon for the biosynthesis of purines, thymidine and amino acids. Catalyzes the irreversible conversion of 5-formyltetrahydrofolate (5-CHO-H(4)PteGlu) to yield 5,10-methenyltetrahydrofolate. It can also use 5-formyltetrahydropteroic acid (5-CHO-H(4)Pte) and 5-formyltetrahydropteroylhistidine (5-CHO-H(4)PteHis) as substrate. (6S)-5-formyl-5,6,7,8-tetrahydrofolate + ATP = 5,10-methenyltetrahydrofolate + ADP + phosphate kcat is 2 sec(-1) for cyclo-ligase activity with 5-CHO-H(4)Pte. kcat is 3 sec(-1) for cyclo-ligase activity with 5-CHO-H(4)PteHis. kcat is 5 sec(-1) for cyclo-ligase activity with 5-CHO-H(4)PteGlu and 5-CHO-H(4)PteGlu(5). Monomer. Belongs to the 5-formyltetrahydrofolate cyclo-ligase family.