I want to know what happens when I press the trigger. What signals are sent to the mount?
I'm asking because I want my camera to trigger a flash that I'm building myself.
The large center pin is the main thing (along with the ground connections at the edges) on a standard hot shoe. The smaller pins are for proprietary communication between a specific camera brand and flashes compatible with that brand's automatic flash protocol.
If you are creating a self made flash you only need to be concerned with the center pin and ground connections.
When the camera's shutter is released by pressing the shutter button all the way down the shutter begins to open. When the first shutter curtain is fully open exposing the entire sensor at the same moment (if the shutter speed selected is slower than the camera's flash sync speed), the connection between the center pin and the ground is completed inside the camera. When this circuit closes it allows voltage from the flash to flow through the camera and back to the flash where it causes the flash to discharge the energy stored in the flash's capacitor(s).
A word of caution about using a home built flash with your expensive DSLR: When a charged flash is connected to a hot shoe and the hot shoe completes the circuit a lot of voltage can flow through the camera's circuitry. If the voltage supplied by the flash is higher than the camera can tolerate, you will probably irreparably fry your camera's circuitry, or at least those parts connected to the hot shoe.
Different cameras have different flash voltages they are designed to tolerate without damage. Some can only handle a few volts in the 6-10 volt range. Others can work with flash output voltages of 250 volts or more. Check the specifications for your camera and do not allow more voltage than for which your camera is rated to flow through the hot shoe! There are voltage reducers available, but even those can be overloaded beyond their specifications. The one linked above is rated to reduce up to 400 volts to less than 6 volts.
If you would mention your concerns, possibly some answer could address some specifics.
There are many signals at the Nikon hot shoe. The smaller pins conduct ongoing active communication (Nikon system is named CLS) between the camera and the flash. The flash is told values of f/stop and ISO to display (and the flash can compute and show maximum flash range). Lens zoom can zoom the flash. Flash can signal its mode and any compensation, etc. One small pin is a quench pin, to be sure to stop the flash when the shutter closes (flash is pointless if shutter is closed).
TTL: At the shutter button, the camera requests a TTL preflash from TTL units, and after the camera meters that preflash, then a metered flash power level is set into the flash. The Nikon Commander (not on D5300) can involve multiple flashes individually (lighting ratio, etc).
One major use is the large center pin. The camera shutter shorts that pin to ground to trigger the flash in sync with shutter. This shorts the flash sync voltage from the flash, signaling to the flash to trigger then.