Short answer is no. A fifth wheel weighing 7600 will have a pin weight of around 1500 loaded over your rear axle (based on 20 percent pin weight factor). Add 200 lb for hitch, and anything else you load into truck including passengers. Now check the max payload on your truck per sticker in door jamb. My guess is you will well exceed the truck payload ratings. Forget tow ratings (what truck will pull). What is more important is what the truck is designed to carry. Personally, I wouldn't tow with that set up.
Steve Rinker
Rochester, NY
2013 Keystone Sydney 340FBH 5th Wheel, 12,280 lbs loaded (scale)
2015.5 GMC Sierra Denali 3500, SRW, Duramax, CC, Payload 3,700 (sticker- not scaled yet)
Take my posts for what they are, opinions based on my own experiences.