the domain, is the values for "x", namely the values used up over the x-axis.
the arrowheads on the lines, indicate the graph continues, upwards and to the sides, so it keeps on going to infinity.
however, let's notice that the values between -3 and 5, are not used up, those are not part of the graph, and therefore, are not part of the domain, however -3 and 5 ARE part of it, whilst all numbers between them are not.
using interval notation
( -∞ , -3 ] ∪ [ 5 , +∞ )
it's notable that the ∞ signs have a parentheses, reason being, is a number we never touch because we don't know what the last number is :).