Honda will have a premium because they have a reputation or are perceived to be more reliable.
5k for a hatchback will get you a car that is barely 25% into its life of what 7 years? Of trouble free driving.
I wonder if the stats for reliability between the top 80% are that variable. And it is more dependant on random chance of picking up a dud, or lack of service history.
Logically best bang for buck would be the most common car you would think, avoiding any that falls into badge prestige territory.
So, I would be looking for a Corsa or Focus. Anything with <1.2 engine and a turbo would make sense too.
Edit: OK Corsas and Focus look a bit pricey. I’d maybe look at a Skoda Rapid Spaceback or Hyundai i30.