I am having a similar problem with my iPhone 5. When I first got the iPhone 5 I synced it with my old Mac mini. Since then my old Mac mini broke forcing me to purchase a brand new Mac mini. Now I am trying to sync my iPhone 5 with the new Mac mini and it seems like the the only option I have is to erase my iPhone. None of the work abounds that I found on the net apply to me because I am unable to access the old Mac mini that my phone is synced with.
What can I do about this? I have a lot of photos, videos and GarageBand files on my iPhone 5 that I am not willing to part with. Between the time that my old mac mini broke and now, my iphone has been my computer so everything I have done in the past 5 months is on this phone. I have been a loyal apple customer for over 15 years. I just dropped another $1000.00 on a new Mac mini just to be rewarded with being told that I have to erase my iPhone before I can use it with my new computer. That kinda *****. If there is any way around this problem please let me know.