First, it might be important to note that Plantinga is not Reformed in regards to predestination. Plantinga is a molinist when it comes to that. My point in bringing this up is to make sure that no one confuses what Plantinga means by reformed. Plantinga does not reject natural theology, in fact, Plantinga uses it. This can be seen in virtue of his 12 or so good arguments for the existence of God and his development of the ontological argument. However, Plantinga (like the reformed) argues that one does not need any arguments in order to be rational and warranted in their belief in God. He argues as Calvin does that man has a sense of the divine. That is to say, our cognitive structure is built in such a way that belief in God is produced in a basic way (no need of any arguments). Thus, Plantinga's main beef is with evidentialism, and not Aquinas and his big 5. So be rest assured, you can accept both Thomism and aspects of Reformed Epistemology.
The evidential objection to belief in God is that if one is without a good argument for belief in God than they are not rational in holding their belief. Thus, in order to actually have knowledge that God exists, one must have a good reason for that belief. This is grounded in what is known as classical foundationalism. Classical foundationalism avoids the epistemological regress argument by postulating the concept of basic beliefs. That is, there are beliefs that do not need further justification and all other beliefs are based upon those basic beliefs. The basic beliefs according to classical foundationalism are those beliefs that are self-evident, incorrigible, or evident to the senses. Thus, in virtue of belief in God not fitting into any of these categories, one must have an argument for it to be considered justified and rational.
Plantinga rejects classical foundationalism for a few reasons. Plantinga first accuses classical foundationalism of being self-referential incoherent as classical foundational does not meet its own criteria. Plantinga does not believe that classical foundationalism is either a self-evident belief, an incorrigible belief, or a belief that is evident to the senses. He further argues that the truth of classical foundationalism cannot be proven in virtue of building on these basic beliefs either.
Secondly, Plantinga demonstrates that there are more beliefs that need to be taken as basic than the ones that classical foundationalism endorses. For example, the belief in other minds does not meet the criteria of classical foundationalism and yet one would be irrational in not holding to that belief. Perhaps one may argue that it is in virtue of seeing the effects around them that they come to an inductive conclusion that there are other minds, as a sort of best explanation. However, upon further thought, there appears other explanations that explain just as much and possibly even simpler. For example, perhaps one can explain the effects around them by postulating a Freudian theory, that in order to survive in this cold and dark world our cognitive faculties produce the belief that there are other minds around us. Or maybe, there is an evil demon monster who is playing a trick on us and gives us the illusion that there are other minds. Another possibility could be that the individuals who we come in contact with are actually zombies but they give the same effects as other minds.
Similar arguments can be made regarding the beliefs in induction, memory, testimony, and the external world. Thus, Plantinga argues that the basic beliefs espoused in classical foundationalism are way to strict and would leave one to be irrational in accepting obvious truths that are found in the above beliefs. Furthermore, if there box becomes wide open regarding what constitutes a basic belief, Plantinga postulates that belief in God and Christianity should be considered a basic belief.
Plantinga argues that belief in God can be basic in the following way. If there is a personal loving God who is there and has created man in His image so that He may know and love them, it would appear that something like the sense of the divinity would be true. That is, upon being in God's ordered creation (the right epistemic environment), belief in God could be produced by man's cognitive faculties in a way that allows man to know this personal God. Meaning, man could know God without an argument as one might just come to the conclusion that upon looking at the stars in the sky that God created them or perhaps after one commits a great sin, one just finds their self believing God is upset with them. It appears that if God uses these things to make Himself known to his creation, then man can form belief in God in a basic way. This of course is conditional, that is, if Christianity is true, then it would most likely be warranted in virtue of the reasons given. This means that Plantinga is not arguing for De Facto but De Jure. Plantinga then takes naturalism and famously argues that unlike Christianity, if naturalism is not true, it most likely would NOT be warranted. For a brief primer on that check out my blog here http://furtheringchristendom.files.word ... tion-1.pdf