Hi MayDay! I feel you on not wanting car hassle.
I was just recently looking up used cars with my daughter. Shiny clean Prius with around 50-70K miles for $10-12K? There are gazillions of them for sale in my local area, and the supply keeps going up and up and up from what i can see. You can narrow by color and still have tons of choices. Most are at dealerships. Buyer's market in cars right now, as others pointed out. I agree that a $5K car can be pretty sketch (although I recently bought a $3K prius that I drove for several years without problems), but a $10-12K used small car is typically pretty sweet.
It's kind of like wine: a $3-5 bottle is hit or miss, to be generous, but a $10-12 bottle is WAAAY better tasting most of the time.
Nothing wrong with buying new, but autotrader.com is your friend as well.
$5k will buy a fairly nice and reliable subcompact economy car.
$5k will also buy a luxury truck or SUV that is completely worn out and will cost thousands per year in repairs.
Looking at craigslist, $5k will buy a ~15 year old toyota or honda sedan or hatch with ~150k miles.
If I'm driving a 15 year old car with 150k+ miles, it's a car I have made sure has been properly maintained because I am the original owner (or the second owner with nearly all of those years in my hands).
OR, I'm hard up and a such a vehicle is the only vehicle I can afford. Otherwise, it's not worth it.
You might be overlooking a lot of cars with at least 50k low-maintenance miles left in them. My search (min year = 2010, max mileage = 100k, max price = $5k) revealed the following, not including all the Ford Focuses out there or anything with a problem declared in the ad:
2013 Chrysler 200, 66k, $4300
2012 Nissan Altima, 91k, $3890
2011 Buick Regal, 97k, $4200
2010 Saturn Outlook, 99k, $3900
2012 Ford Fusion, 92k, $4999
One can expect the models listed above to last until about 150k before you're likely to have major trouble. Yes, a Honda or Toyota would go 200k before major trouble, but that's also why they are outrageously expensive as used cars. Either way, a person driving 10k miles per year gets 5 years of transportation.
In any case, brand selection is no reason to commit financial harakin by running to the new car dealer.