The five points are the rebuttal to the five articles, but you are missing the fact that Arminianism is of Calvinistic trajectory (it is Calvinism except where it departed).
There are people who believe men are born with the ability to turn to God if afforded the opportunity. This is a denial of Arminianism by definition (it denies articles 3 and 4). But it is also a denial of Calvinism (it denies total depravity).
My argument is that all five points or articles are essential to the theology of each camp, otherwise they would not have been expressed. A denial of one of them is a denial of that theological system. There is no such thing as a 4 point Calvinist. A Calvinist who is moderate is moderate not because he rejects an essential doctrine of Calvinism but because of his stance on how that doctrine is defined. If you reject Limited Atonement then you are not a Calvinist because you reject Calvinism as it has been defined. There is no such thing as a 4 Article Arminian either. If you reject total depravity as defined in the articles of the Remonstrants, then you reject Arminianism. If you reject the idea of predestination as defined by Arminianism, then you do not belong in that camp.
I guess that makes me "Mister Nowhere Man" except of course I know where and with whom I am going.
HankD