Catalyzes the methylation of 5-hydroxyuridine (ho5U) to form 5-methoxyuridine (mo5U) at position 34 in tRNAs. 5-hydroxyuridine(34) in tRNA + S-adenosyl-L-methionine = 5-methoxyuridine(34) in tRNA + H(+) + S-adenosyl-L-homocysteine Homodimer. Deletion mutant does not contain mo5U. Binds magnesium, but the ion is dispensable for mo5U forming activity. Belongs to the class I-like SAM-binding methyltransferase superfamily. Cation-dependent O-methyltransferase family.