Catalyzes the formation of 5-methyl-uridine at position 54 (m5U54) in tRNA. S-adenosyl-L-methionine + uridine(54) in tRNA = 5-methyluridine(54) in tRNA + H(+) + S-adenosyl-L-homocysteine Belongs to the class I-like SAM-binding methyltransferase superfamily. RNA M5U methyltransferase family.