I want to know how to change the serpintene belt on a 2005 Chevy Trailblazer

A six cylinder Trailblazer does not use a timing belt. It has a timing chain.
Are you sure you did not cause a problem with the cam or crank sensor ?

Usually the noise is a belt. The surface of the belt changes as it warms up.
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it can be a number of things ac clutch idler pulley trencher alternator power steering water pump and belt most likely is an old belt because its stiff and slips when cold it warms up the belt is more flexible and it grabs beater the trencher can be weak and with the cold belt it can slip

Here is the serpentine belt diagram for a 1996-1998 Chevy truck with the 4.3, 5.0 and 5.7 liter engine. Removing the belt is very simple. Using breaker bar and a socket that fits the center bolt of the tensioner pulley

Hope this helps...

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it has a chain if it is a v8 or v6.

Sounds like your water pump is going out or your thermostat is stuck. Check the thermostat first and make sure it is not frozen in the clsed position.

make sure you have the correct length belt for that model.

If the belt was slipping or became contaminated with oil or coolant that should resolve the problem. Check the belt tension first before replacing the belt

sound like possible fuel filter has some dirt in it you are suspose to change every timr you change oil or the fuel pump is over heating when you drive it try the filter first the