Speaking from experience of buying budget cars for daughters
resist at all costs buying cars that are interesting
to you - those will come back to bite you in the ass. You'll be sorry with anything European for this type of car - ask me how I know! Today's generation does not care about cars the way we did - they are appliances to them. So buy the most bland appliance you can find. Honda or Toyota are sure bets. $5000 is going to buy you a 10-12 year old Honda or Toyota with 150,000+ miles - still lots of life left in those. I would also consider a plain-jane Taurus or Impala. Hundreds of thousands of these have been driven 200,000 miles+ by salesman/rentals/employees. The reliabilty is good (the build quality? Maybe not, but your daughter won't know the difference).
I would not limit the search to under 100,000 miles. 200,000 miles is the new 100,000 miles for cars built in the last 10 years or so.