Catalysis of the reaction: 5,6,7,8-tetrahydromethanopterin + N-formylmethanofuran + H+ = N(5)-formyl-5,6,7,8-tetrahydromethanopterin + methanofuran.
formylmethanofuran:5,6,7,8-tetrahydromethanopterin N5-formyltransferase activity