Niko covered it in most parts, AF will not work otherwise on D5000/3000/60/40.
The exceptions are couple of motorized lenses but you don't want these trust me, they are too slow.

With one or two exceptions it's easier to just remember that any lens that says "HSM" will work. "Hyper Sonic Motor" is the Sigma equivalent to Nikon's AF-S.

I thought I would pass this list along. I was looking into maybe getting a Sigma lens so I emailed Sigma customer service to see what lenses were fully compatible (would autofocus) and they sent this list back.

4.5mm F2.8 EX DC HSM CFE

10mm F2.8 EX DC HSM FE

30mm F1.4 EX DC HSM

8-16mm F4.5-5.6 DC HSM

10-20mm F4-5.6 EX DC HSM

10-20mm F3.5 EX DC HSM

17-50mm F2.8 EX DC OS HSM

17-70mm F2.8-4.5 DC Macro HSM

17-70mm F2.8-4 DC OS HSM

18-50mm F2.8 EX DC Macro HSM

18-50mm F2.8-4.5 DC OS HSM

18-125mm F3.8-6.3 DC OS HSM

18-200mm F3.5-6.3 DC OS HSM

18-250mm F3.5-6.3 DC OS HSM

50-150mm F2.8 EX DC HSM II

50-200mm F4-5.6 DC OS HSM

12-24mm F4.5-5.6 EX DG ASP-HSM

24-70mm F2.8 IF EX DG HSM

50-500mm F4-6.3 DG APO OS HSM

70-200mm F2.8 EX DG Macro HSM II

70-200mm F2.8 EX DG OS HSM

70-300mm F4-5.6 DG Macro (motorized/model 5A9306)

70-300mm F4-5.6 APO DG Macro (motorized/model 5A8306)

70-300mm F4-5.6 DG OS

120-300mm F2.8 EX DG HSM

120-400mm F4.5-5.6 DG APO OS HSM

150-500mm F5-6.3 DG OS HSM

300-800mm F5.6 EX DG HSM

50mm F1.4 EX DG HSM

150mm F2.8 EX DG Macro HSM

300mm F2.8 EX DG HSM

500mm F4.5 EX DG HSM

800mm F5.6 EX DG HSM