Pictures out my window

The first is the pretty yard across the street. It's what I see when I sit at my computer or talk to my students. The second is, unfortunately, what I see when I look up at the eaves right outside my window. Obviously when the former occupant patched the water damage she didn't actually REPAIR the source of the problem. This patch fell down within a week of our moving in here, after the first good rain storm. There is also a wet patch in the ceiling in the hall . . . .