Here is a solution that worked for me. My scenario is somewhat different, as my son had an iphone 4s that had to be replaced (I replaced a failed component inside it - never again!). So I bought a cheap but new iphone 5 online, and went into the AT&T store to get them to use their punch to reduce the sim card to the required size.
Iphone 5 tells him that the sim card is locked, so he went to the AT&T store where they told him that he needed a new sim. This would have required me to go to the store, he couldn't do it himself as the account was in my name.
Well I searched on line, rebooted the iphone multiple times, cleaned the contacts with rubbing alcohol, all that good stuff. No go, either no sim message, or sim card locked message. Out of curiosity I got out my prehistoric Nokia that takes an enourmous sim card and centred the tiny sim squarely on the contacts. No sim detected. As a final test, I turned the sim card 180 degrees and it worked!
Turns out that Einstein in the AT&T store had used the punch incorrectly to cut the sim card down to size. When I cut a tiny corner off the sim on the opposite corner of the card from the sloped corner so that it would fit in the iphone 5 card holder and put it in the phone, eureka!
I bet that many sim cards have been unnecessarily replaced on iphone 5s just because it is not clear to which way to place a bigger sim in the card cutting punch to reduce them to the correct size. This is obviously not a solution for those of you with sporadic drop outs, but might help someone who has had their sim card cut to size by a monkey!
