Why my nikon d5100 doesn't auto-focuss with a sigma 70-300mm?
Why my nikon d5100 doesn't auto-focuss with a sigma 70-300mm?
Does the lens have an internal focusing motor?
Some lenses for the Nikon mount - those made for older cameras - did not have their own focus motor, but relied on the focus motor built into the camera.
Your camera is a newer Nikon, and has no internal focus motor, but relies on the lens to have it's own motor. In Nikon'speak, these are called AF-S lenses.
I'm not sure what Sigma calls their non-motor and motorized lenses, but you should see which version you have.
Advanced Nikon DSLRs (D7000, etc) have an internal focusing motor so they retain autofocus compatibility with older lenses, but the entry level cameras (D3xxx and D5xxx) can only autofocus with the newer lenses; regardless of whether or not they are made by Nikon or 3rd party.
If this is not the issue (i.e. The lens does have it's own motor), then perhaps autofocus is switched off on the lens.
Is the lens returnable. Besides not autofocusing, the cheap 70-300mm lenses are not very good.
In case you didn't get the memo, the D5100 does not have it's own built-in autofocus motor. To autofocus with this camera, you should use lenses with built-in autofocus motors. With Nikon lenses, they are marked as AF-S and AF-I models. With Sigma, the only sure way I see is to get a lens with HSM printed on it.
If your Sigma lens doesn't have "HSM" as part of its description then it doesn't have a focusing motor in the lens and thus it can't auto focus on your Nikon D5100.To make the D5100 more price competitive Nikon deleted the focusing motor from the camera body which requires the more expensive Nikon AF-S lenses or third-party lenses which have a focusing motor in the lens.
Although a very nice camera, she needs a lens with a built-in motor.