After the strain on their friendship during Book 4 and the Triwizard Tournament, things between Harry and Ron are mostly back to normal. While Ron is a target of Harry's bad temper just like Hermione during Book 5 (mostly thanks to Ron’s new prefect status), he still spends Book 5 being Harry's most loyal supporter.
When Seamus Finnegan shouts, "I don't want to share a dormitory with him any more, he's mad" (11.155), Ron (as prefect) steps in and warns Seamus that he'll get detention if he doesn't shut up. And at the end of the novel, when Harry insists that they have to go right now to the Department of Mysteries to find Sirius, Ron backs Harry up against Hermione, who thinks they should wait. (Unfortunately, Hermione proves to be right. But Ron's faithfulness is still nice.) Because Ron is so solid in Book 5, his story lines mostly fall to the background. Ron provides an excellent foil to Harry's adolescent angst in this novel.
Twice in Book 5, something unheard-of happens: Ron gets something that Harry wants. In Book 4, Ron got jealous because Harry was appointed Triwizard Champion. Things always seem to happen to Harry – but not so much, in this book. First, Ron gets made a prefect (a student who is supposed to monitor the behavior of other students). Harry didn't really want to be a prefect, but he can't figure out why Ron would be more deserving of the post. After all, Harry faced down Voldemort last year – shouldn't he at least get a prefect's badge in recognition of how much he has done in the war effort?
Harry does feel bad about secretly resenting his best friend like this, but he can't help it. Harry's bad feeling about the prefect thing dissipates when he sees Mrs. Weasley confront a Boggart that keeps transforming into the dead bodies of her family. Harry remembers how dangerous life is during wartime, and by the end of Chapter 9, he is ready to let go: "it seemed extraordinary to him that barely an hour ago he had been worried about [...] who got a prefect's badge" (9.311).
Second, Ron becomes Gryffindor Quidditch team Keeper now that Oliver Wood (former team captain) has finished school. Meanwhile, Professor Umbridge gives Harry a lifetime ban on Quidditch for attacking Draco Malfoy at the end of a Gryffindor-Slytherin match. So, Ron gets to play Quidditch while Harry doesn't.
Getting to play Quidditch isn't such a great thing for Ron, though, who turns out to be a rotten player whenever anyone is watching. Not to mention, he gets worse each time he makes a mistake, so when things go wrong for Ron on the Quidditch pitch, they go very, very wrong. Ron also has to stand up to the Slytherins, who recognize how sensitive he is to criticism. They start singing nasty songs about his Quidditch performance every time he plays, which makes everything worse.
In the final game of the season, Ravenclaw vs. Gryffindor, Ron manages to pull himself together. He overcomes his self-consciousness and his lack of confidence to perform beautifully on the pitch. And thanks to Ron's performance, Gryffindor wins the Quidditch Cup. Ron does manage to learn something about himself over the course of Book 5 – it's just understated and mostly off the page.
A lot of Ron's character quirks are played for humor in this book, again, as a foil to Harry's deadly seriousness. He's amusingly overprotective of his little sister, Ginny, who, he is horrified to learn, has started dating. Ron takes an immediate dislike to Ravenclaw Quidditch player Michael Corner when he hears that Ginny is going with Michael. When they break up, Ron suggests, "Well, I always thought he was a bit of an idiot [...]. Good for you. Just choose someone – better – next time" (38.217). Ron looks at Harry when he says this, so maybe he's got his heart set on a Ginny/Harry pairing.
Ron gets horribly injured in the last battle with the Death Eaters in the Department of Mysteries, when he takes a spell that leaves him confused and out of it. He starts grappling with a tentacled brain that seems to be crushing his chest. While Ron's character often offers light comic relief to the serious things going on in the book, Ron's courage in the last battle shows how important his loyalty and good faith will be in the battle against Voldemort.