When you say you're getting a used Series 5, is this from Apple or a 3rd party? I'm not sure if the standard AppleCare warranty will transfer over for watches bought from a 3rd party. If it has AppleCare+ then it can be transferred, but I think the previous owner needs to submit the request to do that. (I've transferred AppleCare+ for a Mac I sold on eBay before.)
However if you buy it from Apple in their refurbished / clearance store then it will come with the same standard warranty as if it was new, plus you have the option of buying AppleCare+.