yes you may be in trouble. the quoted hitch weight is with an empty trailer, no propane in the tank(s), no battery(s) installed no water in the tanks. So I suspect your "guess" of 500-700 lbs is more realistic and will likely be over 600 once loaded.
As an example our trailer had an advertised tongue with of 750lbs, which I verified was correct when empty. Once we put on 2 batteries, filled the propane, loaded the trailer with our stuff and fill the fresh tank, tongue weight is 1450lbs! If fresh tank is empty and grey black near full it's up over 1500lbs.
Vehicle mfg "assume" 10% hitch weight when doing their calculations on capacity for towing. Trailer mfg design to near 15% tongue weight. See the disconnect!
And more than likely that "5,000lb" towing capacity assumes the tow vehicle has a driver, full tank of gas, no passenger and no luggage. Passenger weight and luggage weight subtracts from towing capacity.
I don't know which transmission the subaru has, but if it has a CVT, that's another potential reliability issue if overloaded. CVT's are great for many applications, reliable, low loss, etc. but they currently haven't been able to be designed to handle heavy load applications on a continual basis. If it has a CVT that may be the limiting factor on towing.
Similar issue on vehicles with DCT transmission especially w/o a torque converter in front of the transmission. to easy to burn up the clutches when towing. (Don't believe subaru uses and DCT's)
2011 Keystone Outback 295RE
2004 14' bikehauler with full living quarters
2015.5 Denali 4x4 CC/SB Duramax/Allison
2004.5 Silverado 4x4 CC/SB Duramax/Allison passed on to our Son!