OP, I'm a certified CPST (car seat tech) and I concur with those that have given you kudos for asking!
To clear up some things, because there's been a bit of misinformation in this thread:
At 5.5, *some* 'typical' kids are ready for a booster, and some are not. Once you move to a booster (or booster mode on a combination seat) the CHILD has to do the work of staying in position in order for the adult seat belt to do its job. In a harnessed car seat, the SEAT does that job. If your kiddo is a less mature 5, and delayed, staying harnessed for a while longer is a good choice.
As others have pointed out, height is just as (sometimes even more important) than weight when considering a combination seat (FF harness + booster).
The standing height limit (ie: max height stated as 52") is NOT negotiable, and is, in fact, an absolute just as the stated weight limit (i.e. 65lbs, 80lbs). But there's a THIRD way in which seats are outgrown, and that is when the child's shoulders go above the top slot or 'click' for the seat (aka 'torso 'height').
What I'd suggest, before you do anything else is confirm his weight, standing height (back against wall, measure from floor to top of head) and torso height (sitting with back against wall, measure from floor to top of shoulders).
With that info I can better tell you what seats are outgrown or close to outgrowing, and what seats he'll have more growing room in. Both the Britax Frontier and the Graco Nautilus 80 are great seats. Though the Frontier Clicktight (newest version) has such a great install if it's in your budget and he's still got height growth room, I'd go for that personally as you'll appreciate the easy install.
Also to consider: He doesn't necessarily need to be harnessed in every car. Let's say dad takes him to/from school a few times a week. Short trips. If he can sit properly with instruction for short periods of time, a booster is totally appropriate for those times. So you can have an extended harnessing seat for every day and trips, and a booster for short trips or emergencies. That may help with your budget. And provided he can sit right for short trips, and the booster gives him great belt fit, it's a very safe option for a 5.5 year old.
The Britax Parkway is nice, but if he's a chunky kiddo he may not be as comfy as it's a narrowed seat. The Diono Monterey is wider with movable side wings and might be a more comfortable choice.