S-adenosyl-L-methionine-dependent methyltransferase that specifically methylates the C5 position of cytosine 72 in tRNA(Thr)(TGT) and tRNA(Cys)(GCA). In vitro also methylates tRNA(Thr)(AGT). Methylation requires, in the acceptor stem region, the presence of the 3'-CCA terminus, the target site C72, the discriminator base U73, and the second and third base pairs (2:71 and 3:70) in the tRNA substrates. cytidine(72) in tRNA(Thr) + S-adenosyl-L-methionine = 5-methylcytidine(72) in tRNA(Thr) + H(+) + S-adenosyl-L-homocysteine cytidine(72) in tRNA(Cys) + S-adenosyl-L-methionine = 5-methylcytidine(72) in tRNA(Cys) + H(+) + S-adenosyl-L-homocysteine The PUA domain plays a role in tRNA recognition through precisely recognizing the CCA end and the D-stem region of tRNA. Belongs to the class I-like SAM-binding methyltransferase superfamily. RsmB/NOP family.