The D40/60/3000 (same basic camera, essentially), is a great body to learn how to use a DSLR. I started on a D60, myself (10mp vs the D40's 6mp).
I know you said you're ready to move up from your p&s, but depending on how you see yourself using the camera, a DSLR may or may not be worth the several hundred bucks.
Just for family vacation/sight-seeing snapshots? I'd take a look at a high feature super-zoom camera. They have many of the features and manual controls that a DSLR has and are also easier to maintain than DSLRs.
Looking for the ease of full control and superior low-light capability that a DSLR offers or you're looking to pursue photography as a new hobby? Yeah, go for a DSLR.
The D5000 is an interesting specimen. High quality CMOS image sensor, but does not possess an internal auto-focus drive motor, which in your case probably isn't important.
Long-story short....if you see yourself keeping the camera set on the 'green box' i.e., auto-mode, and never using the manual/semi-manual modes, then I'd go for a high feature super-zoom. Otherwise, as an entry-level camera, the D5000 would work just fine to cut your teeth on using a DSLR.