You can swap that motor in, but your going to have some issues. The first issue is mounts. A B-series anything will not bolt into a CRX. Several companies make mount kits to fit B-series engines into older chassis and most of the bugs have been worked out but they aren't free. From what I've heard, HASport seems to be one of the better ones out there.

Second issue, tranny. A B18C5 comes stock with a hydro tranny (meaning the clutch is moved by a hydrolock system, like your brakes). A CRX use a cable to activate the clutch. I've heard of people converting a EF (or '88-'91 Civic or CRX) to hydro, but it never works out right. The easiest solution is to use the a cable tranny from a JDM 1st gen B16A. I believe they are very close in gearing to a B18C5, but may have a lower final drive (just from what I've read). Some JDM trannies also have factory LSD's, but it won't be as new as a B18C5's would be.

Third issue, ECU. A B18C5 will have an OBD II ECU while your car is a pre-OBD car. That means the ECU will not plug into your in-car harness and is basically useless to you (but very valuable, B18C5 ECU's are hard to come by). You can use the JDM 1st gen B16A ECU, but your fuel maps won't be perfect and the fuel cutoff about 400-500 rpm earlier. I've read about a reprogramable ECU from Zydne that is for EF/pre-OBD cars but I don't know much about it.

Scare you out of it yet? It is possible, but it won't be simple. For the same amout of headches and money, you could probably just buy a complete JDM first gen B16A, a mount kit to make it fit and stuff it with new pistons/rings, a new set of good cams/valvetrain along with some head work and a tunable computer (and maybe even a new aftermarket LSD) for just the cost of a B18C5 and run circles around just about anything out there. Save up a little more, skip the cams and head work and go with a turbo if your interested in raw power. B18C5's are great motors and very powerful right out of the box, but not always the most cost effective solution.