This.
Check the battery to make sure its vent hoses are still connected.
Check the frame rails for any damage, some people thing they would make a great jacking point, only to find out that the frame rails crumple if you try to lift from them.
I'd bet that there is someone on Miata.net who'd go with you to check out a potential purchase and give you a more experienced, first-hand perspective in exchange for a beer. I know I would if you were shopping around the NH area.
The NA Miatas, 1990-1997, are considered the best "Miata" whereas the NB 1999-2005 and NC 2006-2011+ are considered progressively better cars while (perhaps) losing a little bit of the spirit that makes a Miata so much fun. If you can live with the basic NA features, I think that's what you should get.
With a $5k budget I'd (personally) be looking for a good condition, rarer NA, like a 1991 BRG, 1994-1997 M edition, a Sunburst Yellow, or a 1993 Limited Edition

awe

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I would steer clear of the 1990 to early-1991 short nose crank cars unless you're confident in your mechanical abilities.