My iPhone won't transfer purchases to my computer because I'm not authorised when I am?

My iPhone is authorised to an old family account on an old HP laptop I had. I just bought a macbook and I made a new account because my old one was already authorised to 5 computers. My computer recognises the phone, and none f my music is appearing in my library. But it will not let me transfer any of my purchases, saying my computer's not authorised when it is? I've tried so many times but it keeps telling me to authorise the comp, which I have done, and then I'm back at square one. I would appreciate any help ye can give me! :/

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