Make sure battery is fully charged. Plus, 5 days is a long time for it to drain a battery. Are you saying that if you tested the battery after 5 days it shows no voltage? Or are you saying if you let it sit for 4 days the engine would start? Have you monitored the battery over the 5 days to see how much voltage it is losing?
Attach a digital multi meter between the battery negative and the end of the negative cable. Set the meter to read milliamps. Keep in mind that you have "keep alive" draws on your rig. Computer memory, radio clock....etc, so you should see some milliamp draw when you hook up. If the battery is not fully charged during this process, it should be.
I know on newer rigs there is a larger milliamp draw than what I used to see when I was in my shops. I used to use 50 milliamps as a threshold. I would say your 97 Tahoe qualifies as an older rig. Anything over was not good. If you are over that start taking fuses out one at a time and when you see the higher milliamp draw go away then the work begins. You need to find out what components are on that fuse circuit and start disabling them one at a time to find the culprit. There may be only one component on that fuse or multiple items. The first thing I always did before I even started pulling fuse was unplug the alternator to see if the draw disappeared. Usually easy to get to and was a culprit many times. It could be simple or difficult but the initial set up, as I explained, is to get you ready to diagnose.
Others here will chime in.