New imac and iphone -- but itunes says I have already authorized 5 computer

I purchased a new imac and iphone this weekend. My old mac DIED -- completely fried but fortunately I had backed up my photos and music. Now when I try to sync my iphone it says I have already authorized 5 computers (which I didn't -- I only owned 2). It's driving me nuts every time I connect my iphone to the BRAND NEW, 3 days old, imac. After spending quite a tidy sum on Apple products in one day the least it can do is work properly.