I've always loved fun on a budget, maybe because I'm poor.
Anyway, throw out your favorite fun cars (or trucks) for
under $5000.
I'll start............
Obvious one: Miata. Ha, I beat you all to it. Blast to drive, reliable, cheap. Too bad I don't like convertibles.
Honda CRX Si: pretty much the same attributes as the Miata, but FWD and prone to rust. Also fits you into the "ricer" mold.
Saab 900 turbo: some may find this to be an odd choice, but my '97 900SE was a really fun car. 2.0 turbo has very little lag, and can be easily modified for silly power. Good ride, decent handling, can be made much better with a little work. Reliable, good MPG, cheap parts. I would lump both the NG900 and original 900 into the same description, but the older ones are even cheaper. I'd love to find a decent SPG as a daily driver.
BMW E30: 325is is what a BMW should be. Lightweight, tossable RWD car with a straight six in front. 318is isn't as fast, but still fun. Engine swaps or forced induction can make an E30 into a giant killer.