2005 avalanche fan runing truck is off

There is a resistor in the fan circuit to give you different speeds and it burns out. It's down by the fan on most cars.

check if the ac indoor unit is above 6ft if so it will not regulate as the cold air will not get high enough to make the thermostat work
another possible reason is that the thermostat has failed
get out a technician to do a proper diagnosis

I would point to either the thermostat sticking or the fan clutch going bad

Could be your coolant temperature sensor is faulty,here's a link on how to replace.

My first guess would be a restriction in the radiator or a faulty bearing in the fan motor.

2005 Chevrolet Avalanche 1500 Service & Repair Manual

2005 Chevrolet Avalanche 1500 Service Repair Manual Software Download...

LICENSED OEM SERVICE AND REPAIR MANUAL SOFTWARE FOR THE 2005 CHEVROLET AVALANCHE 1500!

If you need a repair manual for your Chevrolet, you've come to the right place. Now you can get your repair manual online in convenient digital format. Old paper repair manuals just don't compare! This online repair manual software covers the Chevrolet Avalanche 1500 and is perfect for any do-it-yourselfer.

In the dark old days of auto repair, you had to buy a traditional service manual in book format which would retail at a higher cost. Getting the same information in digital format is so much less expensive and more convenient!

Maybe you need the manual to fix the brakes on your Avalanche 1500, or possibly replace some worn out suspension components. Or you might need to get your engine running, or just do the required standard maintenance. Whatever the case may be, this repair manual software for the Chevrolet Avalanche 1500 is just what you need.

You will have all the service information you could ever need for your vehicle. It will help you fix the brakes, engine, suspension, steering, drivetrain, electrical problems, heat, air conditioning, etc. Anything can be fixed!

You can save a lot of money by working on your own vehicle. You probably already know this, but mechanics charge a lot. Do it yourself and use this 2005 Chevrolet Avalanche 1500 repair manual software to guide the way.

It gives you the manual for your Avalanche 1500 and it's very easy to use. It is compatible with any Windows computer including desktop PCs, laptops, smartphones and tablets.

License includes 1-year access to OEM service and repair procedures and unlimited access to supplemental data.

so it is a bad blower ( relay )
replace it will work fine

Make sure there are no coolant leaks. Check to see if the cooling fans are working and there is nothing blocking the front of the radiator. If these look ok then it might be time to have the radiator cleaned or replaced.

Motor switch has gone out, most likely due to high load on level 5. Replace switch and I suggest lubricating blower motor bearing to help take the strain on the system.

The best place for that info is to call a GM dealerships parts department they can tell you in a matter of seconds.