Convertible cars under $5000 aren’t so easy to find because price ranges for convertible cars are generally higher than for common cars, so the choice of really good models is quite limited.
Used convertibles for sale under $5000 are mostly soft-top convertibles or manually operated hard-tops. The age of the car will be around 15 years (which is, however, not a problem for time-proven models). Buying an automatic transmission will save you up to $2000.
Mazda MX-5 Miata (1999-2004). This car is generally among the cheapest and at the same time most favored and top rated soft-top convertibles. While the newer retractable hardtops of the same model will cost you something like $20000, soft tops aged 1999-2005 can be purchased for $4000-$5000. This one is more responsive on the road than other models in the same price range, gets overall positive responses and is frequently referred to as the best deal for the money.
Chevrolet Camaro (1997-1999) is another time-proven popular choice. Overall high customer satisfaction. Leaking roof is the most common issue. Cheap interior is probably another disadvantage. Less aggressive front than with other muscle-cars from the range. However, with the same money you can get newer models if you look at Mazda MX-5 Miata or Ford Mustang - the next on the list.
Ford Mustang (1998-2001 models) can be bought at a price-range $3700-$5000. The car has two major disadvantages: inferior interior with not very convenient drivers position and average handling characteristics. Probably not the best model for a woman for it’s rather crude characteristics. A muscle-car icon, Ford Mustang is a love-it-or-hate-it vehicle. No complaints concerning maintenance or unpredictable or unexpected issues from the owners, however, and for many this is the only convertible model they would have for a lifetime.
Another option for those shopping for used convertibles under $5000 is salvage cars or rebuilt cars of later years or more expensive models. These can actually be purchased for this or even lower price. Just keep in mind the following: