The short and sweet rundown . . .
The D5000 is basically a D90 in a smaller lighter weight body. It has a trendy flip screen. Both have video. But unlike the D90 it can not work with any/all lenses, especially older lenses (like Will mentioned above). That’s not unimportant because we all stumble across older bargain-basement lenses now and then and it is nice to know they can work on your camera body.
The D5000 is basically a high-end replacement for the D40 entry level body whereas the D90 is lower-end replacement for the D300 prosumer level body.
The D5000 is a big screen D40 and the D40 sells for half the price.
The D5000 is a great camera as are all the Nikons. The flip screen is just one more thing I would end up breaking because moving parts are a recipe for disaster for me.