y=2^3-4=5

(Are you sure you're typing this right?) There is only one value of y. Thus if one value of x satisfies the equation, the equation is onto... however, in this case, every value of y is 5 so it wouldn't be one-to-one.

If you mean y=x^3-4, this is one-to-one. You just have to prove y = n for some x. (HINT HINT Plug in for y).