Set the Shutter Release to one of the 2 available Burst modes. See page 4 of your D5300 Reference Manual.
Unfortunately, Nikon made a change with the D5300 manual eliminating an the Index and a lot of other information common to all previous Nikon DSLR manuals such that the D5300 Reference Manual sucks and is the worst, most user unfriendly manual Nikon now provides with one of their cameras.
But, Nikon knows few people that have ever bought one of their 'compact' entry-level DSLR cameras use the Reference Manual effectively. So first Nikon stopped providing a hard copy of the manual with their 'compact' entry-level DSLR cameras, and now they leave out a majority of the information an advanced user would find beneficial.