2017 FR Wildcat 28sgx

[w2drfg]

We were out looking at 5th wheels today and really liked the 2017 Forest River Wildcat 28sgx floorplan with a huge size shower. Its UWR is 9,049 and the GVWR is 11,978. My TV is a 2007 Chevrolet Silverado Classic 2500 Ext cab SRW 4X4 6.6 Duramax Turbo diesel where it appears to be max towing capacity of 13,000.
It looks like adding a slider hitch will max out the safe towing with this fifth wheel.

Can you comment on this combination. Is it safe to tow or should I look for less weight?

[w2drfg]

Here is more information on this rig.
dry weight is 9449
Gross weight 11,978
Hitch weight 1578
Cargo weight 2529