A friend of mine -- we'll call him Rich -- was complaining today that he can't edit the contacts on his iPhone. That ever since he upgraded to iOS 5, the Edit button in the top-right corner of the Phone or Contacts app went missing. After a quick search through Apple's forums, I found the cause.
Turns out the problem has to do with iCloud. Rich didn't feel the need to enable any apps to use iCloud, including Contacts. And therein lies the problem. For whatever reason, the Edit button goes missing for some iOS 5 users because they didn't allow iCloud to access their Contacts.
If you have a missing Edit button, you simply need to go to Settings > iCloud and move the slider to On for Contacts.
Next, tap Merge and the Edit button will return to its rightful place, in the upper-right corner of the Phone and Contacts apps. You can go back and turn Contacts off in iCloud, and the Edit button will remain.
I tested the above method and can say with certainty it works. There is also a method that will let you edit your contacts, but I haven't tested it (because I had already reinstated the Edit button on Rich's phone). If you are vehemently opposed to using iCloud, it might be worth investigating. Instead of using iCloud to bring back the Edit button, you can supposedly use the Messages app to edit contacts. When viewing a text conversation, scroll all the way up to the top until you see the Call, FaceTime, and Contact buttons. Tap the Contact button and, according to Robio7 in the Apple forums, you'll see an Edit button.
Of course, I'm getting to this fix a bit late. Your best option at this point is probably going ahead and upgrading to iOS 6.
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