The following post is taken almost verbatim from my way of explaining S5 to people. It makes sense to me, but I recognize not everyone will agree. In any case, I take it to show the thesis “whatever is possible is necessarily possible” is correct.
It seems to me that if something is possible, it's necessarily possible. Take a world, W1, and take the proposition P. Now let's suppose the metaproposition "Possibly, P" is true in W1. A necessary and sufficient condition of possibility is that it [whatever is under consideration] appears in some possible world. With that in mind, let's consider the denial of S5. The positive claim of S5 is that if something is possible, it is necessarily possible. The denial entails that if something is possible, it is not necessarily possible (you can place the negative operator prior to the whole thing as "it is not the case that" and you will yield the same result). This denial means that there is some possible world where P is impossible. Call this world W2.
Here's where the fun begins! In W2, then, P is impossible. But what does it mean for P to be impossible? If "Possibly, P" means that "in some world, P appears (or is true)," "not-possibly P" (or P is impossible) means that in no world is P true (or appears). These definitions of possibility and impossibility are what we're working with as stipulatives in modal logic. Basically, if this is not what possible and impossible mean, I don't know what they are supposed to mean!
So with that in place, we can now derive a contradiction: P is true in at least one world (W1) and true in no worlds (per W2). Whatever is a contradiction is a necessary falsehood. Call the derived contradiction "The Impossibility Thesis." This means that in no world is The Impossibility Thesis true, including W2. But if in even W2 The Impossibility Thesis is false, then, necessarily, either "possibly P" or "not-possibly P." But this process can be repeated, with identical answers, for every possible world. But in that case, what we have described, whichever answer we grant, will be a necessary truth. In this case, it's "Possibly P."