1. His diary. Not since Owen got the safe code from it. One Abbadon is enough for any lifetime, even Jack's. Besides, Ianto might think that turnabout is fair play, and there's no way Jack wants anyone seeing some of the notes he's made.
2. The 3D glasses that Torchwood recovered from a London television shop in the 1950s. The energy signature on them was a dead giveaway, but even Jack hasn't figured out what he's supposed to be looking at.
3. The picture of the team from Gwen and Rhys' wedding. He's moved it to the top of the filing cabinet, from where Tosh and Owen still smile down at him.
4. The picture of Gwen and Rhys from their wedding. It was probably mean of him to take it when they were still, er, comforting each other after the shock of the whole exploding alien thing. The bottom drawer is definitely a more appropriate location.
5. The coral he's been growing. It needs more space nowadays.