I replace mine every two years but then I haven't been climbing much. Seems to me like when I climbed all day year around I would get a new rope every 6 months but I can't remember for sure. According to one climbing book I have they say either dynamic or static rope should not be used after 7years of manufacture regardless if it's ever been climbed on or not. However, both the Author says, and I have used rope much older then that on occasion. I have one repelling line that's almost 15 years old that I just used it last month, however it's been stored in the house and only been used 3 or 4 times before.
To the guy with the pics,
I'm sure it's fine and I've seen a lot worse being used, but when it's starts looking like that it's time for replacement in my opinion. As Bermie said, "peace of mind". Confidence, regardless if in a tree, riding a sportbike, hiking in remote areas, etc, etc, is important and in a tree the last thing you need to be focusing on is wether or not your rope is safe. Good luck.