Your GVWR is 10,000. Out of that 10,000 pounds, as much as 5200 can be on the front axle and as much as 6100 can be on the rear. However, if you have 6100 on the rear, the max GVWR is still 10,000 pounds, so the front can only have the difference between the 6100 on the rear and 10,000 pounds, which is 3900 pounds.
The load ratings for the axles aren't directly related to the tow capacity of the truck. The truck is probably rated to tow a whole lot more than it can carry on it's axle ratings. So, tow rating is different than axle ratings. Most TT tongue weights are 10% of the trailer. However, you mentioned a 5th wheel. Those have a much greater tongue weight PLUS the 5th wheel hitch weight itself is considerable.