Based on my six, I would counsel against it. Love love love the car, but repairs are generally around $1k. It sounds like something you would like to avoid. A fantastic ride when running though...

On an up-to-$5k budget, you could get a REALLY well maintained, unmolested, enthusiast owned E30 (up to 91) 325i sedan or 325is; or an even cherrier 318is. Although I would avoid the 1.8l 4 cylinder M42 motor of that vintage due to reliability issues and lack of power. (Although this car is super light and fun!)

I don't know your feelings on going a little bit older, but in my opinion, BMW really had the 3 series dead-on in 1990-1991, in terms of power to weight ratio, size and lack of electronic interference to driver input. They really looked great back then too (well, after the big metal bumpers, anyway.)

At that price point, the attainable e36's would be those in the earlier years (92-95) and with the lower output engine (M42 1.8l - prone to timing cover profile gasket failure, mentioned above) - you might be able to find a few 325's in that price range, but they're probably underloved and undermaintained; or crappily modified. A quick glance at craigslist and you could probably verify this.

As the e30's are getting older, the prices for 325i's and 325is's seem to hold strong for really good examples; whereas the earlier e36 prices seem to be falling. I can't verify that with hard statistics, but I think I've noticed a trend.

Anyway, that's my $.02 - Good luck in your search!

Yah the $$ is about right./ I have had Bmmers for a lot of years not and I gotta say maintainance isn't a big deal. On the older cars you gotta do the timing belts every 60-thou miles but that's not a hard job - take you 4 hours your first time. OIther than that don't flood the car or you'll be in to a new set of plugs and they are pricey. That leaves a major tune up every couple of years depending on how much you drive.

A 95 (or there about ) will likely need at least one CV joint and a stub axle and you can do that in about than an hour.

I have a 94 318 that is a project car. As with all mid-90s 3-series, the most important thing to look after is the cooling system (hence this one now being a project car). I started having problems with the cooling system around 190,000 miles. I also have a 01 that is a blast to drive. Once I get that paid off I'm gonna go for an 07.