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