Concerning dry weight: difference between BP vs 5er

You are not going to like the performance of your truck when towing any high walled RV.

As mentioned half tons and 5th wheels generally don't mix well. At 6k dry, probably more like 8k loaded if you are living in it, you have 1500+ pound of pin weight plus a 250 pound receiver in the bed, plus yourself in the cab. Not many half tons can support 2000 + pounds of payload.