1. Necessarily, something exists. (Premise)
2. There is a possible state of affairs at which nothing contingent exists. (Premise)
3. If something exists and nothing contingent exists, then something necessary exists. (From 1 and 2)
4. Hence, something necessary possibly exists. (From 2 and 3)
5. Therefore, something necessary exists. (From 4 and S5)
Like all ontological arguments, it is really premise (1) that is most controversial. However, I think that the above premise (1) is quite obviously true, and not nearly as controversial as the usual "a maximally great being possibly exists." In its denial of ontological nihilism, the proponent may simply stress that a state of affairs at which nothing at all exists would itself be an existing entity. Of course, this commits us to either realism or conceptualism, the latter of which I prefer.
I would argue further that this necessary entity is a mental concept, which could only be grounded in a necessary mind, e.g. God. However, I don't want to pursue that argument at the moment.
For those skeptical of S5, let's instead consider the following reductio, having already granted the truth of (1) and (2):
Assume (6): a necessary entity does not exist. (6) and (2) imply that there is a possible state of affairs at which nothing exists. However, this contradicts (1), which states that something or other must exist. Therefore, (6) is false, and (5) is true. An appeal to S5, while legitimate, is unnecessary in this case.
Naturally, the Platonist will gladly accept the conclusion of this argument. If he is also an atheist, though, then he will presumably insist that the necessary entity concluded to in (5) is one of the forms, and not a concrete entity, such as God. The debate, then, turns upon whether one should adopt Platonism or conceptualism, but I regress.