With the 2010, you only had 200HP to start with, and there are always a few ponies that escape as time and mileage accumulates. I run 35's on my '13 Rubicon, and 6th gear is just fine. But I'm making more power than you, and have 4.10 gears. Unless your '10 is a Rubicon, you've got 3.73 gears, which isn't exactly helping you any.
If 5th gear is gone, and you have driven it, there is a good chance there is damage to other gears as well. Opinions vary (as they do on most things) but I have never replaced a single gear. If a gear is broke, I replace the whole gearset. Because pieces of broken gear inside the case aren't good for the other gears and I dislike re-repairing things. It's not really a quick rebuild, which drives up the cost if you're paying someone to do it. Swapping in a remanufactured transmission will be quick and easy. You will pay more in parts, less in labor. I suspect the overall cost will be about the same.
Personally, I'd go with the swap, and at 90,000 miles I would also seriously consider replacing the clutch and pressure plate while it's apart.