first, the 10,000lbs. rating is for the receiver ONLY, not for your Tahoe. GM puts that same receiver on a number of different vehicles, all with different towing capacities.
second, if your Tahoe's towing capacity is only 5700lbs., then that's too much trailer.
your 5700 number is rated with only a 150lb. driver in the Tahoe. anyone else and anything else in the Tahoe, lowers that number by its weight.
third, the 23LS has a bogus website "dry" weight of 4700lbs.
this does not include the weights of "options", like awning, microwave, spare tire, oven, a/c and so on.
you can generally add another 400lbs. for the "options", for a trailer that size, making it about 5100lbs. before you add water, propane, battery and cargo.
how did you come up with the towing capacity of only 5700lbs.?