If you're still located on the Key Peninsula, I can give you a few suggestions to at least try ...or at least a good starting point.
First, I personally recommend Roadmaster products. Roadmaster is a northwest-based company that started in Portland and now is headquartered in Vancouver WA. If needed, you'd have better access to their technical support. I've visited their shop several times. It's been quite a few years now since I've contacted them for anything but they used to be very helpful over the phone, by email, or if dropping into their shop in person. Not sure if it's still that way now, however.
Many on the forum will recommend NSA products. I've always used Roadmaster so that's all I personally have experience with during the years we RV'd. I can't comment on NSA as I've never used their products myself. Roadmaster and Blue Ox are the major players but not necessarily the best or your only choices.
If you are not
planning on doing the baseplate installation yourself, there are two shops that I can recommend.
You may have heard of Ballew's in Tacoma. They're a hitch shop that has been around for decades and I've had several jobs done by them through the years. They are top notch in my book but like any business, there are always some who will disagree. They are an authorized Roadmaster dealer but also carry other products too.
Ballew's Hitch, Truck & RV
There's also a place in Bremerton that I've not used myself but have talked to several who have had good experiences. It's called Kitsap Muffler & Brakes. They are also a Roadmaster dealer and in addition to doing muffler, brakes, exhausts, and general automotive, they also have a hitch shop.
Kitsap Muffler & Brake - Hitches
Others can give you more up-to-date information than I have about tow bars and supplemental brakes so don't hesitate to post specific questions if you have them.
eta: and yes, I believe you are capable and have the capacity to tow your Accord as if you've confirmed your hitch rating is 5,000 lbs. and your GCWR minus GVWR is 5,000 lbs., you should be fine.
2nd edit: the tow bar I last used and recommend is the Roadmaster 522 (Falcon All-Terrain with a 6,000 lb. capacity) and Amazon is offering it at a pretty good price right now at $770 (GO HERE
) but you'll pay more if buying it from a place like Ballew's or Kitsap Muffler. However, consider all the other suggestions you get and make your own decision as to what brand of tow bar you settle on. And BTW, a tow bar weighs around 70 pounds (or most will be under 100 lbs.) so it's not too significant as it pertains to your question about the weight of the towing equipment.
3rd edit: I just looked up the GCWR minus GVWR of a 2010 37L (didn't see a 2009 37L) and it's 26,000 - 22,000 = 4,000 lbs. so even though your hitch might be rated at 5,000 lbs., it appears your towing capacity when the coach weight when loaded to its maximum allowed (or i.e. GVWR) is 4,000 lbs.
I still think you'll be fine, however.