A:
The D5300 does not contain a focus motor. It relies on NIKKOR lenses that have built-in focus motors. Nikon denotes these lenses with an AF-S designator for Nikon's Silent Wave Autofocus Motor. If your 70-300 is an AF-NIKKOR lens - it will attach to the D5300, however, you would not be able to obtain autofocus. You would have to focus manually.