First up on your list of focus settings to investigate on your Nikon D5300 is the Focus mode. You get three settings for tweaking autofocusing behavior and one option for manual focusing.
Choose the Focus mode via the Information display control strip. Remember: To activate the control strip, just press the i button.
When the camera is in the P, S, A, or M exposure mode, you can choose from four options, which work as detailed in the following list; in other exposure modes, you can choose only the last two options (AF-A and MF). The exception, again, is the Night Vision Effects mode, which limits you to manual focusing when you use the viewfinder.
AF-S (single-servo autofocus): Designed for shooting stationary subjects, this setting tells the camera to lock focus when you depress the shutter button halfway.
In this mode, the camera won't release the shutter to take a picture until focus is achieved. If you can't get the camera to lock onto your focusing target, switching to manual focusing is the easiest solution. Also be sure that you're not too close to your subject; if you exceed the minimum focusing distance of the lens, you can't focus manually, either.
AF-C (continuous-servo autofocus): Geared to photographing moving subjects, this mode causes the camera to adjust focus continuously while the shutter button is pressed halfway.
By default, AF-C mode prevents you from taking a picture until focus is achieved, just like AF-S mode. But you can tell the camera to capture the shot at the instant you fully depress the shutter button, regardless of whether focus is set.
Make the call via the AF-C Priority Selection option, found in the Autofocus section of the Custom Setting menu. Focus is the default setting; choose Release to allow shutter release before focus is set.
AF-A (auto-servo autofocus): This mode, which is the default, gives the camera control over whether focus is locked when you press the shutter button halfway or continuously adjusted until you snap the picture. The camera makes the decision based on whether it detects motion in front of the lens. Either way, shutter release is prevented if the camera can't focus.
AF-A mode works pretty well but can get confused sometimes. If your subject is motionless but other people are moving in the background, the camera may mistakenly switch to continuous autofocus. By the same token, if the subject is moving only slightly, the camera may not make the switch. So choose AF-S or AF-C instead.
MF (manual focus): Choose this setting to focus manually instead of using autofocus.
On Nikon AF-S lenses, including the 18–105mm lens and the 18–140mm lens available in a bundle with the camera body, simply setting the switch on the lens to M automatically sets the Focus mode to MF.
However, the opposite isn't true: Choosing MF as the Focus mode does not free the lens focusing ring so that you can set focus manually; you must set the lens switch to the M position. For other lenses, check the lens instruction manual for focusing details.