lynn - I doubt you will have any problems. I just mounted a Draw-Tite Class III hitch to my 03 Wrangler and I cleared the spare (30" tire with Canyon rim) with my Sport Carrier carrying my CR500. I probably had about 5-6 inches between the pipe and the spare.
You'll have to do some measuring on the hitch and carrier to be sure. I just lucked out finding a used hitch for $40 rated at 350# tongue weight. The rear shocks on the Wrangler, on the other hand, need a little help. Also, the wheelbase of the CR5 is about the same as the width of the Jeep.