Ok, thanks. A few quick google searches seem to be coming back with anything between 3100 and 5800 tow capacity for your truck. Not really a lot of information out there as most sites are just listing the "Maximum possible towing".
But, the manual listing a GCWR of 7000 lbs tells us a lot. It tells us we can't trust the numbers in your manual. If it's saying the GCWR is 7000, and the towing is 5300, then it's saying that your truck only weighs around 1700 lbs. Those quick google searches are saying your truck weighs between 4900 and 5300 lbs, so your effective towing capacity compared to your manual's 7000 lbs is only 1700-2100 lbs.
Even if we take the low end of 3100 from the various searches I did, 7000-3100= 3900 lbs truck...
Sorry I can't help better with these numbers, maybe somebody else who knows Mazda's better can chirp in. My only experience with Mazda was with my MX-5, which only had a carrying capacity of 300 lbs by spec, but being 240 myself, I know I was always over that 300 limit without any issues.
There's no use crying over spilled milk, unless it's on your keyboard.