This song was originally a track on the Who's "Quadrophenia" concept album, and it's lyrics make more sense within the context of that album.
The album tells the story of Jimmy, a teenager who has long embraced the fashions and music of the Sixties "Mod" movement. But lately, all the things that used to make him happy have become stale or have let him down. In the songs on the album before "5:15," Jimmy has found that his musical idols, the Who, aren't really so wonderful. He's also found out in "Ive Had Enough" that his girlfriend is cheating on him. He's lost his job and has had a falling out with his parents.
Now that he's all alone, he decides to take the 5:15 train to the beach town of Brighton, a place where he's had a lot of fun in the past. During this train ride, he's taking drugs and looking around at everyone. The lyrics to "5:15" reflect BOTH the things he really sees around him, AND his memories of being a fashionable young Mod.
On the train, he sees pretty, heavily-perfumed teenage girls, and observes that the adult conductors are sniffing the perfume and checking out the girls, while sitting quietly and trying not to be noticed.
As the drugs kick in, he starts to reflect on his life. Like his contemporaries, he was born during or just after World War 2. He remembers being bored by his ordinary middle class life and popping pills.
He remembers the thrill he got from dressing up in Mod clothes for the first time. Even though he thought of himself as a virile, macho stud, he dressed in frilly, sparkly clothes and high heels, as all Mod males did.
Jimmy starts to realize that he doesn't really fit in anywhere... it bothers him deeply, but he tries to pretend it doesn't- that's why he asks "Why should I care?"