S-adenosyl-L-methionine-dependent methyltransferase that specifically methylates the C(5) position of cytosine 3782 (m5C3782) in 28S rRNA (PubMed:23913415, PubMed:31428936, PubMed:31722427). m5C3782 promotes protein translation without affecting ribosome biogenesis and fidelity (PubMed:31428936, PubMed:31722427). Required for corpus callosum and cerebral cortex development (By similarity). {ECO:0000250|UniProtKB:Q8K4F6, ECO:0000269|PubMed:23913415, ECO:0000269|PubMed:31428936, ECO:0000269|PubMed:31722427}. This is the function of NSUN5 (NOP2/Sun RNA methyltransferase 5, ENSG00000130305).