The label 'limited atonement' is singularly unfortunate for two reasons. First, it is a defensive, restrictive expression: here is atonement, and then someone wants to limit it. The notion of limiting something as glorious as the atonement is intrinsically offensive. Second, even when inspected more coolly, 'limited atonement' is objectively misleading. Every view of the atonement 'limits' it in some way, save for the view of the unqualified universalist. For example, the Arminian limits the atonement by regarding it as merely potential for everyone; the Calvinist regards the atonement as definite and effective, but limits this effectiveness to the elect.
Don Carson, The Difficult Doctrine of the Love of God, pg 84
I think Carson has correctly diagnosed why I feel uncomfortable with being '5 point Calvinist'. There is something about God not dying for the sins of the whole world that sounds wrong. Carson argues to distinguish instead general atonement and definite atonement over limited and unlimited atonement. He asserts that under the truth of election, one must conclude that when God sent his Son to the cross, the effect would be different to the elect than to all others. This is Definite Atonement.
I think I can agree with that