Tale of Two Misfits
Starts with the carriages in the fifth year. Luna will explain that they are pulled by thestrals, and that she can see them because she saw her mother die. This is the spark of friendship between them, that will later blossom into romance. Luna and Harry begin hanging out, going to visit the thestrals in the woods so they can escape everything going on in the castle. They talk about what it's like being outcasts and ostracized by the students, bonding over it. Luna is also very clever with charms, and during the DA meetings becomes a very talented, if unorthodoxed, duelist.
Harry will try to get together with Cho Chang, but it won't go anywhere as him hanging out with Luna so much makes her too jealous.
Luna will help Harry a lot, both in Potions and in dealing with Professors Snape and Umbridge. She also let's Harry vent to her about the unfair treatment he's constantly receiving from the ministry, professors, and other students. Harry feels comfortable doing this with her because he quickly learns that she will never judge him about anything and is always willing to just be there whenever her friends need it.