No. This lens lacks an autofocus motor, relying on the camera to have one. The D5100 lacks an autofocus motor, relying on the lens to have one. Adding a battery grip does not change this situation.
The D5100 only autofocuses with lenses having an internal autofocus motor. Nikon designates such lenses AF-S, Sigma calls it HSM. Lenses without the motor will only autofocus with the larger and heavier Nikon cameras such as the D7000.
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