As Harry shouts to Professor Dumbledore after Sirius has died, "People don't like being locked up!" (37.131). In Harry Potter and the Order of the Phoenix, both Harry and Sirius spend long periods of time trapped where they don't want to be: Harry gets stuck with the Dursleys over the summer holidays (blerg) and Sirius must stay at Number Twelve, Grimmauld Place all year to avoid Voldemort and the Ministry. Both of them start to go stir crazy from the isolation. Harry, who is only stuck alone for the summer, contents himself with throwing tantrums. Sirius is the one who keeps going out in public even though he is a wanted murderer.
The theme of isolation in Book 5 is not limited to physical isolation. Harry also experiences intense social isolation because few people believe that he is telling the truth about Voldemort rising again. There's almost nothing as isolating as being thought crazy by pretty much everyone around you. What is more, Harry has a unique destiny. According to the prophecy, he is the one who has to kill Voldemort or be killed. That's a totally isolating experience: to be marked for a destiny that no one else around you can share.