Catalyzes the formation of 5-methyl-uridine at position 747 (m5U747) in 23S rRNA. S-adenosyl-L-methionine + uridine(747) in 23S rRNA = 5-methyluridine(747) in 23S rRNA + H(+) + S-adenosyl-L-homocysteine Belongs to the class I-like SAM-binding methyltransferase superfamily. RNA M5U methyltransferase family. RlmC subfamily.