Brian - I tow a 21' Sea Ray (5,000 lbs total for boat and trailer) behind my 5ver and my biggest concerns for your situation would be in the following order:
1. How the hitch weight is distributed along the 5ver frame. Should be a long hitch subframe to distribute this weight almost to the rear wheels of the 5ver frame.
2. The spring shackles (a.k.a. spring hangers). Specifically, the rear shackles will take a lot more lateral load with your heavy boat and trailer. The shackles aren't known to be a strong point towing solo, much less towing doubles. With a 7100 lb. load pushing them laterally in turns, I'd want to beef up the shackles.
3. Springs themselves. You may need to upgrade at least the rear springs to accommodate the extra weight and twisting/lateral forces caused by the large boat.
4. King pin strength and overall frame integrity of the 5ver in this area. Lots of stories of cracked frames up in the king pin area. This is a scary failure since you can't easily inspect this before a trip and the failure will most likely be noticed while you are underway towing. With your heavy load and small 5ver, I'd be concerned here.
5. Hitch rating. You may be fine here with a 15-16K hitch already but its worth bringing up.
You are towing a large boat by single tow standards. In general, I'd feel a bit uncomfortable towing your doubles rig if the weather turns bad, high winds, etc. due to the high weight of your second trailer and the relatively low weight of the 5ver. But this is just my gut talking.
Good luck,
Phil
2005 Cougar 275EFS
2007 Chevy CC, D/A LBZ