The good news is that there are actually some pretty good little cars out there for under 5K! But you have to be careful & do your do your due diligence. Best bet is to buy from someone who has owned the car for at least 3 years and has maintence records.
You have gotten some very sound advice already. I would only add these comments.
1. Don't even look at any sub $5K German kar!
2. As a former owner & affectionato of Hondas, including a Fit I can confidently say (& am backed up by most stats) that Fits are amoung the most versatile, reliable small cars out there. Often reliable beyond 200K. While they command a pretty high resale value, here are a couple good examples available for < $5K.
For under $5K also consider a late model, low milege Ford Focus. Pretty good, underappreciated little cars. With good maintenance can also go 200K without major issues. Parts when needed are relatively inexpensive.
Happy hunting for the elusive but desirable sub $5K ghetto cruiser. Love to hear what you bag!