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.
https://seattle.craigslist.org/tac/cto/d/2009-honda-fit/6655128353.html
https://seattle.craigslist.org/skc/ctd/d/2008-honda-fit-4d/6649982378.html
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.
https://seattle.craigslist.org/see/ctd/d/2005-ford-focus-wagon-low/6654502547.html
Happy hunting for the elusive but desirable sub $5K ghetto cruiser. Love to hear what you bag!