The best way to think about Nikon D3000 and D5000 lens compatibility is that if it will work on a D40, it will work on the D3000 and D5000. If it won't work on a D40, it won't work on the D3000 or D5000.
For Nikon lenses, the D3000 and D5000 require AF-S lenses for autofocus capability.
For Sigma lenses, the D3000 and D5000 require an HSM lens for autofocus.
I'm not sure of the nomenclature of the Tamron or Tokina lenses, but they would require the equivalent of Nikon AF-S to autofocus with these cameras.