How strict are the licencing laws where you are?
2 seat
Convertible
Soft top
Under $4K
OK, here's an off the wall suggestion.
The MGF is 'cheap as chips' in the UK, old enough to be depreciated fully, new enough not to be a classic.
You can pick them up all day long for under $3K USD and then spend $2K USD on importing one.
More seriously. I"d be very hesitant of a $5K C4 Corvette unless the market is very different from SE Michigan. Any $5K C4 is going to need $1-2K in new bushings, seals, shocks etc to be an acceptable DD up here. Really I can't see your shopping starting or stopping anywhere but the best late NA or early NB you can find for $5K. Lot's of cars have depreciated to $5K, but most cars in that range are well into deferred and ignored maintinance territory by then and will need $$"s and time to bring up to what I would accept for a DD. Miata's wear better, are cheaper to buy parts for and easier to work on than just about anything under the sun, so a defered maintinance Miata is easier to make perfect than most other cars.
C4's eat window seals and bushings plus are rattle traps even when new. this is not a criticism, I love C4's, they are the car that made me stop hating automatics. An L98 with an auto behind it is a wonderful set up, lots and lots of fun and feels way faster than it really is due to it's low end stump pulling torque (let's please not get back into the torque Vs Hp conversation again)
Any soft top Camaro or Mustang will have the structural integrity of an over cooked noodle in this price range, although parts are dirt cheap and they are easy to work on. Skuttle shake will be measured in inches. Unlike the Miata a ripped soft top is neither cheap nor easy to replace.
Z3's are likely to be beat to death, they seem to have held value over the last couple of years and your are smoking crack if you think you are going to get an S52 or S54 model in anything other than parts car condition for $5K. Any base model Z3, while being great cars, you are imidiatly going to have to do the complete cooling system and probably shocks and upper mounts (I dont' mean welding up cracks here)
I may be fussier than some, but I don't see stepping into many $5K sports cars that are DD quality outside a Miata.