Q: Need to know if my alternator is bad.

Hey there, thank you for asking about your 2005 Chevrolet Silverado 1500. Disconnecting the battery while the vehicle is running can damage the Powertrain Control Module (aka, vehicle "brain" or "engine computer") or other electrical components due to voltage excursions (excessive high voltage due to the sudden disappearance of the battery as a load). I (and vehicle manufacturers) wouldn’t recommend using that approach if the problem recurs. Not all alternator failures will show up using box store testing machines. Starters are notorious for this. Your starter could be totally non functional due to a worn Bendix drive and yet when you test it on the store tester, it "passes". Heat and load affect the alternator when it is in a running car so it remains to be seen what your results will be. You can easily test at least the output voltage of the alternator on your running car, which you should do now for reference and again in the future if the problem redevelops. If charging voltage of your alternator, as measured on the car, is out of spec now, I would replace the alternator now to avoid future problems. If you would like a mechanic to do this for you, have a certified technician from YourMechanic replace the alternator in your car.