Nikon's documentation says that you may need to update the firmware on a D5300, although a new one might already be updated. In the
Setup menu, under
Firmware, you should see
You can select manual focus mode via the quick menu. On the main control screen (i.e. not in menu mode), press the
i button and then use the directional control to select the item on the bottom row, second from the left. It says one of four things:
MF. Having highlighted it, press the
OK button to edit, then select
MF. Manual mode is now engaged.
To focus to infinity, twist the focus ring to the right. I don't think there's any way to easily tell what the focus distance is, but once you see the stars come into focus you just need to twist a bit more to be sure.
(There are non-easy ways to tell what the focus distance is. When you take a photo with a compatible lens it's written into the EXIF metadata. But I don't think that's one of the metadata items that you can see in the playback menu, so you may need take a photo and then to copy it onto a computer or phone with software which lets you read the metadata).