I have read from many sources that the D5000 is essentially a "bare bones" D90. From a numbers standpoint, they are very similar cameras. They share a very similar (but still different) sensor, are 12.3 megapixel, etc. If you're looking for some differences in the major areas, you're probably not going to find them.
I was faced with this choice myself, and ultimately went with the D90 largely due to some of the intangibles. Here's why:
1. The D90 is a more substantial investment and camera. It is much larger and just felt right in my hands. The D5000 has a smaller body and I personally wasn't a fan of the grip or the layout of the buttons. Your hands may be different, so be sure to try before you buy. I can't stress enough how important that is. As a side note, there is no vertical battery grip available for the D5000.
2. The D90 viewfinder is leaps and bounds better than the D5000. You see 94% of the actual framing through the D90, compared to just 78% of the D5000. In addition, The D90 uses an actual glass pentaprism viewfinder, which is cleaner, clearer, and brighter.
3. The D90 has two command dials for changing camera settings. I can't even begin to tell you how much easier this makes things. Adjustments can be made quickly and almost instinctively without your eye ever leaving the viewfinder.
4. The D90 acts as a flash Commander, whereas the D5000 does not. This is another intangible that may be important to you depending on how you shoot. The D90 opens up near endless possibilities for sync with off-camera flash and lighting.
5. The D90 has nearly double the customization options as the D5000. Again, I like my camera to be just that...my camera...so I use custom settings quite a bit. Both models can assign custom function buttons and the very cool My Menu feature.
6. Lastly, the D90 has a more substantial battery. CIPA standard measures (w/ 50% flash) that the D90 can get 850 shots per charge, while the D5000 is around 510. Personally, I hate investing in and worrying about batteries.
There is a fairly substantial difference in price between the D90 and D5000. Only you can decide if the additional investment is worth it. For me, it was. Feature-wise, they are very similar so it can be an easy choice for the budget conscious. I already had a Sony a330 that I was trading up from. In my view, getting the D5000 would've been a lateral move.