Stock tire size is fine on 6.5" rim- the 3 225/65-17s I just compared on TR say rim width range 6-8" so that shouldn't be an issue at all- they do have a few 215/70s but don't think you need to go that route. I presume this is for winter season set up? If not I think its questionable to go w/narrower wheel. As for your 3s wheels fitting the CX-5 my guess would be yes but I'd double check- I'm sure its been mentioned here several times- or your dealer should be able to tell you too.
Actually this would be for summer/fall/spring tires. The snow tires I have currently are mounted to the stock rims. I don't think it would be worthwhile to unmount/remount the snowtires onto the mazda 3 rims. I called Discount Tires and they said a 225 width would work on a 6.5" rim. So I think I'm going to bite the bullet.