2009 Silverado K5L

I have found a 2009 ext cab LTZ Silverado and all of my research shows to get the max trailering for a goose-neck trailer it needs to have the K5L HD cooling package which is a HD radiator, trans and oil coolers and electric fans. Plus it needs the Z82 HD Trailering Package. It has the Z82 listed in the glovebox and it has electric fans and I can see a cooler in front of the radiator. I can't see another cooler because I didn't have a flashlight and I couldn't tell if the radiator was HD or not. The K5L is not listed in the glovebox. The difference in the towing is 7500lbs without the K5L and 9600 with. How can I know for sure?
Sonny01

If K5L is not listed on the RPO lable, then it is not equiped with it. I'm not sure what the visual difference is between the radiators.

I have found a 2009 ext cab LTZ Silverado and all of my research shows to get the max trailering for a goose-neck trailer it needs to have the K5L HD cooling package which is a HD radiator, trans and oil coolers and electric fans. Plus it needs the Z82 HD Trailering Package. It has the Z82 listed in the glovebox and it has electric fans and I can see a cooler in front of the radiator. I can't see another cooler because I didn't have a flashlight and I couldn't tell if the radiator was HD or not. The K5L is not listed in the glovebox. The difference in the towing is 7500lbs without the K5L and 9600 with. How can I know for sure?
Sonny01

the radiator with the K5L is larger and deeper. the oil cooler would add tow capacity ...these are the details...

RADIATOR,(CORE SIZE 34IN X 19 7/16IN X 2 3/16IN, CODE AYH,5856)(ACDelco #21742).

Thank you guys!