The answer is No. Sure you can get it home. Sure you can pull it. But you will be very unhappy and you may damage the truck.
5000 pounds is the maximum towing capacity, not a planning number. It assumes the truck is empty other than a 150 pound driver. Add your family, dogs, and camping gear and that rating is probably much closer to 4000 pounds.
I know of no 23' hybrids that weigh less than 5000 pounds loaded. Their empty weight doesn't count.
There are a zillion towing "rules" with some requiring a degree in advanced mathematics. I have two very simple rules: The 1000 Pound Rule and the One Ton Rule. Yeah, I made 'em up but the results are as good as the fancy formulas. Simply stated I want at least 1000 pounds more maximum towing capacity than the trailer weighs fully loaded. And for peace of mind I really want an extra ton! You won't be happy towing a 5000 pound trailer with a 6000 pound max-rated truck. You won't hurt it, but you won't like it.
I pulled my 5000 pound Roo 23SS with my 5500 pound rated V6 Explorer for two seasons. I flogged the poor beast up every hill and into the wind. The engine and transmission were never happy. I replaced the Explorer with a V8 Expedition with the HD Tow option, 9000 pounds max towing. Happy towing for this camper. 6000 pounds standard, 9000 pounds with HD Tow. For a 5000 pound trailer. HD Towing package on my Expedition cost me $350 when factory installed.
We all tend to get defensive with someone criticizes our choice of anything.
๐ If you decide to ignore the laws of physics and pull a 23-footer with a country club SUV at least get a transmission temperature gauge and monitor it closely.
-- Chuck