The thing is, you get to pay the bill. GL5 oils can deteriorate brass / bronze gears. I've seen it in OPE gear boxes before. I really don't know whether or not it would be OK to use in your axle. More additives must make it better, right? My LS tractor manual recommends GL4. Branson has a service manual and I would assume a spec. The trick is getting someone to take the time to open the manual. I'm sure many just pour in an off the shelf gear oil and never take note of the differences. Are many of these axles built by a Korean axle manufacturer and sold to LS, Branson, etc. as an assembly?
So the funny thing is, manufactures may or may not use a regular gear oil when the tractor is built. You will hear Deere uses their Hygard, Kubota the UDT oil in the front axle as well. My LS oil I changed @ 200 hours and it was thinner than gear oil. It also would want to vent the oil if it was filled over half way on the safe zone of the dipstick. With the gear oil, I was going to err on the cautious side - but ended up filling it full, and no venting.
So whatever you choose, take the time to recheck the level. Then check it again after you use it as it takes a while for the level to settle in.