I doubt that any natural person will be able to give you a guarantee that at cheap car will allow you to drive for 5000 miles. Most likely the contract can state that individual parts on the car are in a good shape, but even new car dealerships don´t give contractual confirmations that the car will be able to drive without problems for x amount of miles. So my advice would be to rethink this requirement.
Regardless of wether or not you want to heed my advice, can you elaborate on the 20 items you are offering in exchange for the car?
If you have a car for sale I will send you the items through PM, if not then not going to send to anyone else. Also I know that may be true of the dealerships, but they have legitimacy in making deals, so you can assume that the cars going to run smoothly when you buy it. I purchased a car awhile back and although they didn't guarantee any set amount of miles for total coverage of the car they said if there's problems driving it within the first few days obviously they would look into it if there was no evidence of misuse of the car at all. So there's kind of a non-verbal agreement between the dealership and the person that they are covered if any large screw up happens right away due to a faulty car with no fault of the buyers own, but not exactly 5000 miles they guarantee.
There's obviously going to be cases of abuse if anybody were to offer returns on cars for X amount of miles. Like people could replace the parts and bring it back in and say it broke down or something, which is one reason nobody does contracts or anything like that as their is too high a likelihood that someone is going to scam them. This shouldn't happen as much as it does, but sadly in today's world it is and you can't trust a lot of people when trading things. Maybe stuff will change in the future and scammers will go back to being held accountable for their crimes, so people will stop doing it eventually. However, that is not the case now a days and people get away with scamming $1000's and nothing ever happens to them.
I also got scammed $550 a few days ago trying to buy a car and the guy told me "You bought it and all sales are final" when he specifically stated that I would have no problem driving the car 2500 miles, which he said many times. There was no contract I was just going off of his good will that he was telling the truth and obviously he was just looking to scam and get away with the money. I got one mile down the road and the car broke down and he was nowhere to be found. Then he acted like he was in the right to have scammed me when I messaged him over Facebook That's due to law enforcement not doing their job and arresting people who scam or holding them accountable for their crimes. All fraudsters should be held accountable for their actions, whether it's $100 or $100,000. Letting people off the hook for scams by giving excuses why you can't do anything about it or just giving them a slap on the wrist that isn't going to affect them at all is why scams occur so often. It's honestly sickening that people rip people off so much and think they have the right to do it.
Anyway I will change that 5000 mile contract to be more specific about what I actually want from the car. I basically want the car to last me awhile without breaking down or needing any repairs and to know everything, to the owner's knowledge that is wrong with the car to prevent me being in the middle of nowhere, broken down, without anyway to get to where I need to go, due to an engine problem that the buyer was aware of, but didn't tell me about. Obviously if it breaks down due to me driving crazy or getting into an accident I am not going to make the buyer pay for that I just want to be guaranteed to the best of the seller's knowledge that the car is going to run for awhile and not break down on me. I will change the 5000 mile contract clause to something that more clearly represents what I am after, which is to be sold a car that does not have any serious issues that is going to just break down on me when all I am doing is driving through the middle of town. Or worse yet, driving down the highway and the wheel locks up on me and I can't turn going 70 MPH down the road. Avoiding these types of situations is better for anybody in the long run, the person won't get charged with manslaughter for selling a buyer a car with defunct wheel bearings that they were aware of before the sale. And the person buying the car also gets a good deal by not being at risk for a severe problem when driving down the highway at 60MPH, hahaha. If the car is not safe to drive I honestly do want to deal with it, but I am fine with minor problems wrong with it that are not going to be a safety issue when driving down the highway or in large amounts of traffic.
To clarify on the items I am trading for this car: I purchased these items for about $9,000 total, but the resale value of them today is only around $3,000. All of them except a couple are in the exact same condition as when they were purchased and work excellently. The two that aren't only have minor damages and are still fully usable. This is a very good deal to anyone who is interested as these items aren't knock offs, low quality, or broken. They are all high quality items that are still working excellently or that are in excellent shape. 
