I need to download iTune 10.5. How can I do that?
iTunes 10.5 is no longer available for download, not from any legal source, anyway. The versions still available are iTunes 9.2.1, 10.3.1, 10.6.3, 10.7 and 11.0.4.
If I may ask, why do you think you need iTunes 10.5?
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