One problem related to transfer case has been reported for the 2005 GMC Sierra. The most recently reported issues are listed below.
Within 4 months of purchase, was driving at approx. 25 mph when transfer case shifted into 4 high on it's own. Shut off vehicle, restart and able to put back into 2 wheel drive. Happened on and off for a little more than a month when it went to 4 lo while driving at 30 mph through town. Unable to reset. Limped it the 2 miles to dealership for diagnosis. Cost me $1200 to have the transfer case rebuilt. Smoked the clutch pack, burned out 2 bushings and bent shift shaft. Had second issue of shifting on it's own, may 15th, 2014. This time it cost me $500 for the shift motor to be replaced. Second problem, speedometer reading incorrectly or not at all. Been going on for about 3 years sporadically (apparently the little drive "motor" on the back of the instrument cluster, $300 replacement or, found a company to rebuild with new "motors" for under $200). Passlock issues started in Jan 2014, has left me stranded a couple times now. Can't get a good answer from dealer as to how to repair other than "bring it in and we'll hook it to our diagnostic system" (I. E. Pay us lots of money). Also having issue with check engine light on constantly. Intermittent engine miss on multiple cylinders. Rough idle, crappy mileage, but not down on power. Miss seams to go away off idle and not noticeable under load. New plugs, wires, etc, etc, etc. . . . Haven't figured this one out yet. Same answer from dealer (pay us more money please). Lastly, air bag light came on in Dec of 2012. Never crashed or bumped but had to replace left front air bag sensor. Love the truck, currently has 154000 miles but I'm getting frustrated with all the little electrical "glitches" and the dealer won't help a bit without the normal answer, "bring it in and we'll hook it to our diagnostic system". It's dang near $200 (diagnostic charge) just to get my truck in and out without even getting anything repaired!.