Will a sigma 70-210mm lense fit my nikon d5000?

Will a sigma 70-210mm lense fit my nikon d5000?

If and only if it is a sigma lens with a nikon F mount

If it has the Nikon F-mount will fit, but it won't autofocus as the 70-210mm didn't have HSM, Sigma's name for it's built-in autofocus motor. For that, you'll have to look for any of the several different Sigma 70-200mm HSM F/2.8 lenses.