Why doesn't the aperture change when I turn the ring on my Nikon lens?
If you are shooting still images via the viewfinder
1) Because the lens doesn't actually stop down until just before the picture is taken. The camera meters and focuses with the lens wide open to provide a brighter viewfinder and a shallower depth of field, which assists in focussing.
2) Because when using a Nikon D lens with the D5300, you need to set the aperture ring to the narrowest aperture (the highest f-number) and use the camera's controls to select the aperture setting. The camera will use a lever to stop the lens down the instant before the photo is taken while the mirror is swinging up out of the way.
If you are shooting still images or video via Live View
1) Because in the Nikon D3x00 and D5x00 series, as well as many previous entry level DSLRS, the same lever actuates the mirror assembly and the aperture linkage. Once the mirror is up, the aperture can not be changed from the body.
Can I use an all-manual cine lens on my D5300?
If the lens is built to non-AI specifications you can not.
If the lens has a CPU chip that communicates with the camera you might.