The Five Ways found online or even in Aquinas’ Summa Theologica are cursory arguments. The ST was basically an undergraduate text book, the Five Ways are just summaries, and they’re reliant on other background not covered in the same chapters. Furthermore, just reading the Five Ways as written might leave one scratching one’s own head about why the argument is supposed to be convincing, because they’re taken largely out of context that Aquinas’ expected audience would already know. The arguments
do make sense, but it might require resources behind what’s stated in the Summa Theologica before some of them really click.
Ultimately, we do have evidence: that anything exists at all right now. How the concept of God rationally follows from that is what the “proofs” or arguments made by Aquinas and others intend to show.
I don’t know your budget, and I must say you’re not going to find anything as absolute as a mathematical proof (so don’t go in expecting one what you’ll get are rational discussions and arguments from reason), but here are some resources I found personally helpful:
- The One and the Many by W. Norris Clarke - An introduction textbook to Aquinas’ metaphysics. It hasone major scientific example I cringed at, but the idea of that example is that a thing can be more than the sum of its parts
- The Experience of God: Being, Consciousness, Bliss by David Bently Hart - A bit pedantic at times. It doesn’t go far enough in some places, but it does help establish the concept of God a great deal (and eliminate strawman images) and even helps illuminate arguments put forward by Feser
- Saint Thomas Aquinas and the Principle of Sufficient Reason by Scott M. Sullivan - Exactly what it sounds like, interpreting Liebniz’ PSR in Thomistic terms. A good book.
- Aquinas by Edward Feser - A primer on Aristotlean-Thomist metaphysics. Short, could be a bit more detailed, but then it wouldn’t be a primer…
- Five Proofs for the Existence of God by Edward Feser - The “five proofs” are not Aquinas’ Five Ways. Feser presents his own version of arguments made by Aristotle, Plotinus, Augustine of Hippo, Thomas Aquinas, and Gottfried Liebniz. This is actually a very thorough books that, while might be beyond someone who knows absolutely nothing, is written intentionally to not require the metaphysical background and baggage that the Five Ways require. It also makes arguments that bridge the gap between “necessary first cause” and “one omnipotent, eternal, omniscient mind”.
Feser’s description can be cold and analytical. Hart’s and Clarke’s much more personal. I found all useful.
Again, I don’t mean to send you out and spend all your money. But if it’s a topic you are very interested in and have the budget for it… Also, again, let me stress that these books are helpful, but not a complete solution in themselves. If you read these books or other similar ones, it’ll be a journey. I find the arguments rational and persuasive and find atheism to be irrational in light of these arguments, but I can’t guarantee you’ll end up in the same place.