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). {ECO:0000269|PubMed:31361898, ECO:0000269|PubMed:33799331, ECO:0000269|PubMed:34123281, ECO:0000269|PubMed:34556860}. This is the function of ENSG00000099899 (TRMT2A, tRNA methyltransferase 2A).