With a $5k budget, any NBS you find will most likely have the problems you'd associate with any high-mileage vehicle regardless of manufacturer or model.
Front end, suspension, rust, brakes, bushings, electrical gremlins, drive train issues, oil seals, gaskets, etc...
As far as Tahoes and Yukons are concerned, I'd look for evidence of heavy towing or snow pushing as those activities will be sure to have stressed the transmission on a high mileage vehicle. The tranny will be the most expensive of the 'common' repairs you'd face.
Check to see if there is coolant loss with no visible leaks, this may indicate that the heads are the dreaded Castech heads that are known to crack and let coolant into the engine. If the dealer or private seller hasn't recently changed the oil, ask to have it done while you are present and observe the color of the oil. If it is orange-ish, run away from that particular vehicle. This will ultimately lead to a new motor having to be put in if the problem hasn't been taken care of.
There may be other issues more common to the NBS, but those tend to be the most costly.
Hope this helps.