2005 Chevy Trailblazer Misfire cylinder #5

I have been complaining of sluggish and truck burning to much gas. When I take off or back up truck flutters like to much gas is comin out and the jerks car cuts off same thing when backing up. Engine light never came on but took car for service and they said it had a misfire 700 miles ago engine light never came on. Car start to feel like transmission slipping in whern it changes from 1st to 2nd gear. Took car back to shop they tell me it had misfire code cylider number 5 now they are saying I need to replace the value which will run me about $5k more than what the truck is worth. I was told there was a special policy to cover the type of maintenance but the service department cant seem to find the spealial manufacter warranty. Any advice will help