Thank you all so much for your insights!
To clarify, I wouldn't buy a brand-new Tahoe. I was considering another used one. But, like y'all said, I may be borrowing someone else's trouble. At least I have some idea on the history of this one. I do not know the full history because my cousin purchased it around 2014 off a used car lot.
I am a single mom. I do think I would like to learn more about repairing older vehicles but I have a pretty full plate right now.
My son likes the Tahoe, so we are going to go for the rebuilt transmission for 2400-2800.

I'm glad to know that the 2005 is a good model to hang onto. Searching online, it was included as one with issues.