Portrait is a pretty short book, so I was able to polish off part 5 as well today.
In part 5, Stephen outlines his aesthetic theory, which he draws largely from Aquinas. There are some who conflate Stephen's theory with Joyce's, but I think that Joyce intends this section to be something of a joke on Stephen. Stephen spends a lot of time fretting about the fate of the Irish language, which he feels is symbolized by the word "tundish," a word that the English priest doesn't know. But Stephen later realizes that the word actually has English roots, and is not Irish at all. I think that this is a micro version of Stephen's macro struggles to define himself -- he's constantly getting lost in a labyrinth of his own making (like his namesake Daedelus).
He wants to establish an independent aesthetic theory, but ends up drawing on the very Catholic Aquinas (my Penguin edition says that he owes less to Aquinas than to the Duns Scotus, but I think the point is that Stephen thinks that he's drawing heavily from Aquinas, even as he wants to reject Catholicism). Stephen also sets himself up as Satan with his non serviam, but he is also bound by Jesuitical modes of thinking.
In the end, he flees Ireland, but it's hard not to see his ultimate failure that comes in Ulysses, where he returns after a very short stay in France, and to recall Buck Mulligan's claims that Stephen's refusal to take the Eucharist had killed his mother. Even though I think we're not supposed to take Buck seriously (he's Antinous to Stephen's Telemachus), I think that he's addressing a real fear of Stephen's -- that his break with religion has indeed pushed his mother over the edge.