I just bought a Nikon D5300.
Is there a way to preview the frame with its ISO and shutter speed (in live view) before taking the picture?
Unfortunately not. Nikon has yet to implement an Exposure-Priority preview. It's really too bad as this is a good potential advantage when it comes to having a digital preview such as Live-View.
Keep in mind that no camera can perfectly preview exposure on all conditions. Particularly, anytime the flash is involved, the preview cannot predict how the flash will illuminate a scene. Also, very slow shutter-speeds are hard to preview. Many Panasonic cameras allow this but the preview becomes unusable since there is such a huge lag between image refreshes which is why it it Off by default.
The D5300 can not change the aperture diaphragm on the vast majority of Nikon lenses while the mirror is up. This is because the same mechanism that moves the mirror also provides the mechanical movement to stop down the aperture. Thus, to change the aperture setting when the mirror is up, such as with Live View, the mirror must drop down and back up for the mechanical aperture linkage to stop down the aperture in the lens. This is pretty much the case with all of Nikon's consumer grade DSLRs (D3x00 and D5x00 series).
If you bought the D5300 very recently with the new AF-P 18-55mm lens introduced in 2016 you might be able to do this in the future if Nikon updates the D5300's firmware to take advantage of the electronic aperture control of the AF-P lens. But as far as I can tell without actually testing that camera/lens combo, it doesn't seem that Nikon has made a provision in the D5300's current firmware to exploit the possibility. If they have I could find no reference to such in online reviews and comments. The original 18-55mm kit lens for the D5300 was the AF-S DX 18-55mm f/3.5-5.6G ED VR II. That is still the lens being offered with the D5300 at major online retailers that still have inventories of D5300 kits. (The current model is the D5600 introduced in mid-2016 which followed the D5500 that supplanted the D5300 in early 2015.)
For more concerning the difference between lenses with mechanically controlled apertures and lenses with electronically controlled apertures as well as what "E" lenses are available in Nikon's lens lineup, please see this answer to another question. There is also at least one Nikon mount third party lens offered with electronic aperture control: What are the advantages of Tamron SP 85mm f/1.8 over the Nikon 85mm f/1.8G?
At least one other maker uses an electronic aperture control on all of their lenses that allows the camera to control the aperture in the lens via a data link to a servo located inside the lens, rather than a mechanical connection from the camera body. Nikon has started making a few lenses with electronic aperture control, but for now they are mainly their more expensive lenses. All Canon EF lenses made since 1987 have electronic aperture control.
I doubt the D5300 has a true DOF live preview - my D5500 doesn't.
It will also light-balance the screen so you can see it, whatever your exposure is going to be.
Just take the shot & look at it on the screen, tweak, repeat until happy.
If you don't have time to do that, then you didn't have time to check the Live Preview first anyway.
In the live mode it's already being displaying the current shutter speed and the iso. please carefully check it.