Catalysis of the reaction: 5,10-methylenetetrahydrofolate + tRNA containing uridine at position 54 + FADH + H+ = tetrahydrofolate + tRNA containing ribothymidine at position 54 + FAD+.
methylenetetrahydrofolate-tRNA-(uracil-5-)-methyltransferase (FADH-oxidizing) activity