The domain is the range of x values for which the expression has a definite value.
In this case, the expression isn't defined when the denominator is zero, that is, when:
x(x+3)(2x-5)=0, so that gives us x=0; x+3=0, x=-3; 2x-5=0, 2x=5, x=5/2 (or 2½).
So the domain is x∈(-∞,∞) but x≠0, x≠-3, x≠5/2.
This can be written x∈{(-∞,-3), (-3,0), (0,5/2), (5/2,∞)}.