It’s true. It meets your specs and there are a million of them on the secondary market so the cost isn’t that high.
No way under $5k in any kind of drivable shape.
Someone upthread mentioned the C4 generation Corvette and that could be an intriguing option. I don’t believe they made a convertible model until 87, but 84-86 all have the removable targa top. C4s get a bad rap in some circles but they’re still pretty quick and I actually think they look sharp.
And you can probably a decent running C4 Vette around the $5k range. Not gonna be a show car, but none of these are at $5k.
My choice would be anything MG and Triumph as a secondary. I have experience with and connections to both brands. But those people who said Miata have a point.
Truer words were never spoke.
That is the truth! If I only had 5K to spend, I wouldn’t burn it on some old car. I get my motorcycle first, then if there’s money left over for a fun car, all the better.
I just took one in on trade at the Subaru store where I work. We’ve got it online for $19,000. It’s a base 2004 with 60k miles on it. It is SWEET to drive, but those things hold their value so well. And are scarce, and unmodified ones scarcer still.
Link: New Subaru Cars & SUVs For Sale in Fairfield, OH | Busam Subaru
Also, I agree about the Miata. I have driven several and they have all been an absolute riot to drive. Talk about a grin generating machine.
Another car you might look out for is an older, higher mileage convertible 'Vette. Also very fun cars. I’m thinking something from the early 1990’s. It’s actually kinda hard to find a 'Vette with a ton of miles on them, most are pretty low miles because they’re Summer cars.
How has nobody recommended the Pontiac Fiero yet? Lol. For all I know they were great cars, but mid 80’s cars weren’t often super great.
Miatas have been highly recommended by everyone I’ve ever known that had one.
the cars from the last model year ('88) with the V6 were fairly good, but any of them with the 4-cylinder (a cast iron lump known as the Iron Duke) were miserable.
but then again, it was conceived as a “sporty” commuter car, not a sports car. and as was typical for GM back then, by the time they got it right they killed it.
It also was prone to engine fires…which makes it’s name highly ironic.
only the first year or two, and that was due to a large run of defective connecting rods which would break and “ventilate” the engine block.
Also, it wasn’t a convertible, which the OP would prefer.
My friend in high school’s mom had a gold 2M6 Fiero, she’d never let us drive it, ever. Also, there are a decent amount of convertible conversions out there.
I found this article, it’s absolutely hilarious: This 1986 Pontiac Fiero 2M6 Convertible Asks $2,800, Has Killed
When I was looking at for the same type vehicle as the OP, I researched and test drove an older RX-7 and a convertible Miata. I settled on…A 1st gen (1985 in my case) Nissan 300zx. I have now had 2, a non-turbo and a turbo. Get the turbo. The cars are a blast to drive, virtually zero turbo lag and love curves. They are also pretty darn dependable for a 30+ year old car. No convertible available, but driving with the T-tops off is pretty darn close.
In the words of a trusted mechanic friend of mine “A Miata is a sporty car, a 300ZX is a sports car.”
Gotta repeat - anyone looking for a fun, unusual, cheap, dependable hobby car, really oughta at least check out Corvairs.
Sorry, just when I was looking for a fun hobby car, I was shocked at the quality of car you could get cheap. In fact, even tho I could afford considerably more, a LM would still be on my short list of classic cars I’d love to have.
I’ve got a '91 MX5, the original model, before they starting dicking with the styling and they got plump and unwieldy. They’re reliable, cheap to run, parts are easy to find, and they can’t be beat for sheer fun on a winding road and a sunny day, when the roof is down and you’re playing Gaslight Anthem loudly and chopping through the gears. I used to own a 1966 MkII Triumph Spitfire, and while it was a pretty little car, it was for people who liked speding weekends with grease under their fingernails: a joy when it was working, a chore when it wasn’t. The MX5/Miata is basically a 60s British sportster for people who like their cars to start in the morning. Make sure you spring out for the hardtop, though.
As much as I always admired the styling & muscular stance of the TR4 / TR5 (and the ‘Americanized’ TR250), I fear that 140+ mph in a TR250 is a bit outside the realm of possibility. It should take (cube-rule approximation) about 2.2 times the horsepower to reach 140 mph over the listed top speed of the TR250 (107 mph). I imagine that any speed over the ton was a total hoot in the TR, but 140+ ? Cable-driven speedometers were very optimistic at high speed so that may be a part of the story. 
Thank you for the math. And you maybe correct. It was a long time ago. And the fish always get larger with each tale.
But the NHP did stop me.