The body on the CJ5s are fairly easy to pull, even by yourself. If you have an engine hoist, it's easy to balance, if you take your time. The enclosed photos are of a '53 M38A1, the body structure is identical to your 5, but the military did use a larger transmission access panel that enabled you to pull the body without pulling the steering shaft or even the steering wheel. I pulled it all as one assembly, meaning the front clip and hood for the simple reason I was just interested in using the frame for a jig to ensure that I was getting all my body mounts correct on another project body. I didn't have the original frame at the time because it was off to have all the driveline completed by the owner. We had purchased the one pictured for spare parts, but the body was too good to separate. It was later sold as a restorable unit, sans the engine and transmission.
I used the bucket on my backhoe to remove mine and I'll probably use it to set the new one back on. Will have to be more careful going back on. Take all those covers out of the floorboard. On mine, the wiring was junk so I didn't have to worry about saving it, I just cut it out of the way. Easy peasy.
I'm not 100% sure on the CJ5s, but I would almost put a dollar on that your transmission tunnel cover is the small style that just covers the top of the transmission. The military cover is a three piece cover that consists of a base piece that covers part of the driver's floor, to the passenger side just down Bellow the transfer case levers. The second piece mounts to the front of the first piece, and covers the opening on the lower firewall. The third piece is the traditional CJ style of cover topping the covers.
The civilian cover requires you to at least remove the steering wheel.