My engine has a rough idle why?

Inspect and test the coolant temperature sensor and the idle air control valve then report back-

Might want to check the lower intake manifold gasket. Very common on these. Might want to follow this bulletin. Subject: Cold Engine Idle Misfire or DTCs P0171 P0174

Models: 2002-2005 Cadillac Escalade

1999-2005 Chevrolet Avalanche, Express, Silverado, Suburban, Tahoe, Trailblazer

1999-2005 GMC Savana, Sierra, Yukon

2003-2005 Hummer H2 99 through 05 GEN III truck engines may experience any of the following:

A cold rough idle that diminishes as the engine warms up.
Possible DTCS P0171, P0174, or P0300.
Random misfires at idle. The intake gasket seals may be leaking around the intake ports, causing a lean condition. The intake gasket seals may leak around the bottom side of the port, making it a challenge to detect the vacuum leak. The technician may also notice lower than normal MAF readings if the intake seals are leaking.

If leaking intake gasket seals are found, replace the intake gaskets. During the repair be sure to use the current GMSPO part number for replacement intake gaskets. The current GMSPO part number for intake gaskets will have a teal green intake gasket seal. The old version of the intake gaskets were orange in color. Use only the teal green colored gaskets for a repair.
The intake plenum should also be checked for excessive warpage that may cause an uneven clamping pressure of the seal. If the plenum is found to be warped it will need to be replaced. Service Information states, "An intake manifold with warpage in excess of 3 mm (0.118 in) over a 200 mm (7.87 in) area should be replaced". Intake warpage is measured at the gasket sealing surfaces, and should be measured within a 200 mm (7.87 in) area. This measurement is across only two of the intake runner port openings. Measurements taken across the entire distance of all four intake runner ports will lead to unnecessary manifold replacements.
Let me know what you find.

What you first need to do is determine what is causing the check engine light to come on. What I recommend is having the computer scanned at a nationally recognized parts store. Most will do it for free. With the trouble code they get, we will know why the light is coming on and why it is giving you trouble.

Have that done and let me know what you find.

Joe

Sorry for the late reply, my first thought was vacuum leak. At idle, a vacuum leak could be very noticeable at higher rpms, not so much.

You could check for dead cylinder, at idle very noticeable, at higher rpms you might notice lack of power probably not much else.