Anyone have an older truck they are looking to sell?

That's 20 yr old truck territory. So you're looking at gen 1 Tundras only.

looking at a 2013 Tundra under 120k miles and it may cost me $20k

I found some 20 year old Tundras with 250K miles that were in the price range. Great vehicles but reliable is a hard word to use in that price range. Maintenance and repairs will most likely be needed. You going to drive it 5K miles a year? 15K? 25K?

Bought my high school daughter an '01 Z71 with 180k miles for $3500. Needs paint but runs and drives great. If you only look at what you really need a vehicle to do, there has been very little advancement in the last 20 years. I'd put the actual driving experience of this thing at 95% of a brand new F150. She won't be driving this to college, and I'm thinking about getting a paint job and driving it myself when she's gone.

I have a 2008 single cab F150 STX 2wd with 4.6L V8 that I bought a couple years ago in that price range. It has 192k miles, but it's rock solid. It's our Home Depot truck, but I would DD it in a heartbeat if I had to.

I think for less than $5k you are going to have to go the ford ranger route. I hate to be the guy that always brings up ford rangers but they really are cheap and reliable little pickups.You can still find decent ones with 150k miles on them for less than $5k.
My 2005 has 245k miles on it and I put about 100mi a day on it for my commute. It's beat to all hell because my grandpa used it for his fencing business, it's got no A/C because it wasn't optioned with A/C, the headlights are held in with drywall screws and, there is electrical tape holding the tail light lenses together. It has all those issues but I kinda hate to fix them because they were all things my grandpa did and now that he is gone, I like keeping it original to him. I just slip the inspection guy an extra $10.
I sure love driving it since it has the manual 5 speed and feels like a go cart. Another funny thing is that I get a lot more compliments on it than I do my 2021 F250.

Those 5.3 drivetrains in early 2000's can last a long long time.