To use this lens on the OM-D m5, does it need an adapter? If so, which one? Thanks!
I assume that you mean the Olympus OM-D E-M5. No adapter required. The lens has a standard Micro Four Thirds mount.
However, you may be interested to know that E-M5 users are seeing an issue of troublesome purple colored lens-flare phenomena using this lens on the E-M5 camera body inparticular. There have been several recent discussion threads on the DPReview Micro Four Thirds Talk Forum with actual recorded image examples posted, and discussions among competent and well informed E-M5 users.
I would suggest that you investigate and read those discussion threads, as this does seem to be a troubling issue regarding this particular camera-lens combination.