It can depend on the exact methylation (what group in what base)... generally, especially when you know little about the modification, I'd suggest finding MS facility nearby. If you have the MS facilities, it is pretty simple to detect modifications and, later, at least to some extent pinpoint their site.
For some modifications, there are antibody-based kits. If you're working with a m5C, as your project title suggests, I believe there are some protocols carried over from DNA methylation detection to RNA (such as based on disulfite, see Article RNA cytosine methylation analysis by bisulfite sequencing
and corresponding kits) but I haven't tried them myself. For more chemical alternatives, I suggest taking a look at this paper:
Article Detection of nucleic acid modifications by chemical reagents