YOu don't need to go to other sites for compatibility information - we have a regularly-updated list of all lenses that will autofocus on the D5000 (and the D3000, D40, D40X and D60) pinned at the top of this Forum
Just a guess, but maybe you are not so depended on autofocus ability with that lens, especially if you mostly are going to shoot landscape... This because Hyperfocal Distance (HD) at focal length 11mm to 16mm at example f16 should be very easy to focus into (11mm, f16 HD is about 0.4m; 16mm, f16 HD is about 0.8m).
I have no experience of focusing manually with Tokina 11-16mm, but I consider buying this lens even though I own a d5000.
also consider the Tokina 12-24 that DOES autofocus. . .about $499 ($100 cheaper than the 11-16 2.8). . .optics are excellent in both models, I chose the 11-16 because I have a D200 and can AF it, AND I needed a fast wide angle that could function as a lighter "zoom" in a travel kit. . .
ALSO NOTE: at 2.8, it's SHARP in the center, RAZOR sharp, but slightly soft in corners. Through testing, if you get a good copy (I just got a good one after 2 tries this past Aug), the edges sharpen up corner to corner by f 3.5. . .