How much does the DOF preview matter? Is it a must-have on a DSLR?
Do the Nikon D5300 and D5500 cameras have a depth of field preview button?
The D5300 and D5500 bodies do not have the depth of field preview button.
Whether it matters is a personal preference. I never use the DOF preview on my camera (ok, maybe occasionally when shooting macro). With digital you can just shoot and review on the LCD.
There are some limitations around how accurate DOF preview is with wider apertures. See these questions:
With experience you intuitively know roughly how a shot will look, and IMO you really want to review the shot to be sure, so I wouldn't consider it an essential feature.
In my opinion that is a very important feature if you are composing the image using the depth of field as a compositional element. This seems a tautological answer, but may not.
DOF narrows at larger focal length, also at closer distance to subject. Those who use cameras with small sensors, are using short focal lengths because the optics equivalent to normal lens (50mm for 24x36mm format) corresponds to a wide angle lens. That is common in point and shot, and bridge cameras with small sensors and rarely with full manual control of diaphragm, shutter, and focus. Worse to say, that many of such cameras have inner neutral density filters in place of an iris, thus having no way to control DOF.
Those people introduced to photography with such cameras, may pay not too much attention to DOF in their compositions. Those who where introduced to photography with SLR film cameras appreciated the DOF preview lever which closes the diaphragm to the selected f/value. Or wait until the film was developed to see the result.
Another important feature, was a DOF scale in the distance scale in the focusing ring. Which appeared as symmetric color lines around the distance pointer, each color corresponding to an f/stop. That allowed to focus the subject, to later refocus according to the desired aperture. For example, an f/16 to obtain a clear focus from some point before the subject, but still having a nice bokeh behind the subject.
The D5300 has not a DOF preview button which mechanically close the diaphragm to the selected f/stop. More over, the inexpensive G lenses, like the 18-55mm included in the kit, neither has those DOF scale lines in the focusing ring. It seems that the only way to check that is by using the live preview feature, through the LCD screen. But that is something that we should corroborate, because that is what I was searching when I found your question. To me that is an important, because DOF is part of the compositional elements that I use, and the reason that I want a DSLR, because the inexpensive cameras are very limited in such features. The D5300 can be buy with discount, after the D5500 release. It seems a very good camera, it is in the line of the best non professional Nikon cameras, the D7xxx, line is the lowest of professional cameras. Given the expensive price of the cameras with DOF preview, I don't give too much weigh to that feature in my decision, after all one can view the taken picture or an approach with the live-view feature. with the saved money one can buy other lenses, trying to find some with a distance scale ring with the DOF scale.