Involved in folate metabolism. Catalyzes the irreversible conversion of 5-formyltetrahydrofolate (5-FTHF) to yield 5,10-methenyltetrahydrofolate. (6S)-5-formyl-5,6,7,8-tetrahydrofolate + ATP = 5,10-methenyltetrahydrofolate + ADP + phosphate Magnesium. It can also use divalent cations such as manganese, calcium, zinc, iron, cobalt and copper. kcat is 0.94 sec(-1) for cyclo-ligase activity with 5-FTHF (at pH 6 and 37 degrees Celsius). kcat is 0.99 sec(-1) for cyclo-ligase activity with ATP (at pH 6 and 37 degrees Celsius). Monomer or homodimer. Belongs to the 5-formyltetrahydrofolate cyclo-ligase family.