S-adenosyl-L-methionine-dependent methyltransferase that catalyzes the formation of 5-methyl-uridine in tRNAs and some mRNAs (PubMed:31361898, PubMed:33799331, PubMed:34556860). Mainly catalyzes the methylation of uridine at position 54 (m5U54) in cytosolic tRNAs (PubMed:31361898, PubMed:33799331). Also able to mediate the formation of 5-methyl-uridine in some mRNAs (PubMed:34123281). S-adenosyl-L-methionine + uridine(54) in tRNA = 5-methyluridine(54) in tRNA + H(+) + S-adenosyl-L-homocysteine a uridine in mRNA + S-adenosyl-L-methionine = a 5-methyluridine in mRNA + H(+) + S-adenosyl-L-homocysteine Belongs to the class I-like SAM-binding methyltransferase superfamily. RNA M5U methyltransferase family.