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This may sound silly, or maybe you've already tried it, but, try signing out of your Apple ID (Settings>iTunes & App Store>, click on Apple ID, on pop-up click "Sign Out"), do a power cycle (not sleep mode), then come back here and sign in, try again.

I also read again how Apple states AirDrop works, perhaps you do need to be on the same wifi network, not sure.

Have you sent the others your contact info? Try giving at least one person your contact info via text/imessage, have them add it to their contacts. I say this because, even though the other had my contact info already, this worked.

A shot in the dark: are you able to iMessage with them ok? If not, perhaps you need to turn iMessage off/on to reset the settings.

If nothing helps, a trip to the Apple store if you're close, perhaps there is some hardware issue with your 5s?

I don't need any sort of contact info (as far as I know) because I'm using the "Everyone" option of AirDrop, not "Contacts Only". I can iMessage the two phones fine (well actually just one of them because I don't even have the other iPhone's number).

I'm guessing the Apple store is the best bet, although I really want to know why this is happening.
AirDrop drops to everyone as I see it, no option to single out one specific user...so for me airdrop is useless.

I would be afraid to use it once since this appears to be the way it works.

Tap on one user to send the file only to them...
 
This may sound silly, or maybe you've already tried it, but, try signing out of your Apple ID (Settings>iTunes & App Store>, click on Apple ID, on pop-up click "Sign Out"), do a power cycle (not sleep mode), then come back here and sign in, try again.

I also read again how Apple states AirDrop works, perhaps you do need to be on the same wifi network, not sure.

Have you sent the others your contact info? Try giving at least one person your contact info via text/imessage, have them add it to their contacts. I say this because, even though the other had my contact info already, this worked.

A shot in the dark: are you able to iMessage with them ok? If not, perhaps you need to turn iMessage off/on to reset the settings.

If nothing helps, a trip to the Apple store if you're close, perhaps there is some hardware issue with your 5s?

Ready for the "D'oh!" moment? I logged off and back on to my iCloud account, AirDrop works now! I guess iCloud is required, even for the "Everyone" option. I didn't think I would need to mess around with iCloud at all, I should've listened to you. My idea of "Everyone" was different (I thought it just looked for other iOS 7 devices, regardless of iCloud status).

Very happy, and now I feel a little dumb, lol (I contacted Apple Care).
 
Ready for the "D'oh!" moment? I logged off and back on to my iCloud account, AirDrop works now! I guess iCloud is required, even for the "Everyone" option. I didn't think I would need to mess around with iCloud at all, I should've listened to you. My idea of "Everyone" was different (I thought it just looked for other iOS 7 devices, regardless of iCloud status).

Very happy, and now I feel a little dumb, lol (I contacted Apple Care).
nice, you got it working! ...I only made that suggestion because I was having some issues with iMessage and other things after I went from iOS 6 to iOS 7...seems iOS 7 can be finicky w/iCloud, I signed out and in again and turned iMessages off & on, signed in to Find My iPhone and all those things, then it was fine after this.

I did post it in a previous comment, that iCloud is required for AirDrop, it is on Apples iOS 7 page, in fine print at the bottom. I'm guessing it is somehow used for the encrypted connection between devices (they do use a security protocol so that your data can't be intercepted).
 
nice, you got it working! ...I only made that suggestion because I was having some issues with iMessage and other things after I went from iOS 6 to iOS 7...seems iOS 7 can be finicky w/iCloud, I signed out and in again and turned iMessages off & on, signed in to Find My iPhone and all those things, then it was fine after this.

I did post it in a previous comment, that iCloud is required for AirDrop, it is on Apples iOS 7 page, in fine print at the bottom. I'm guessing it is somehow used for the encrypted connection between devices (they do use a security protocol so that your data can't be intercepted).

I should've tried signing out/in regardless. Apple states that iCloud is required for the "Contacts Only" part of AirDrop (which threw me off). I checked again today and it says it requires iCloud. Happy I have it working now. :) Of course, I'm going to try to AirDrop friends/family again to make sure it's working. Thank you!

Now I'm wondering, what if two iOS devices aren't connected to the internet in any form. Can AirDrop still work?
 
I should've tried signing out/in regardless. Apple states that iCloud is required for the "Contacts Only" part of AirDrop (which threw me off). I checked again today and it says it requires iCloud. Happy I have it working now. :) Of course, I'm going to try to AirDrop friends/family again to make sure it's working. Thank you!

Now I'm wondering, what if two iOS devices aren't connected to the internet in any form. Can AirDrop still work?
No internet connection needed, it uses BT and wifi direct to make a direct connection between the two devices. http://en.wikipedia.org/wiki/AirDrop http://support.apple.com/kb/ht5887 ...hmmm, I see what you're saying, how it's worded here.

Sometimes things seem unrelated but...

If my weather app isn't updating to where I've driven to, usually, if I open something that uses location services such as maps or foursquare, then the weather app finds me. o_O
 
I've done everything including Reset all settings. Logging out of iCloud, and back in.

It simply DOESN'T work.

It would be a lot easier to find answers to this problem if not for the fact that every idiot on the planet thinks its supposed to work from OS X to iOS and keeps making threads and support cases for that NON feature.
 
It would be a lot easier to find answers to this problem if not for the fact that every idiot on the planet thinks its supposed to work from OS X to iOS and keeps making threads and support cases for that NON feature.

I always thought it did that. It's kind of an obvious feature so I assumed it was there. Never made a thread about it though :p
 
I've done everything including Reset all settings. Logging out of iCloud, and back in.

It simply DOESN'T work.

It would be a lot easier to find answers to this problem if not for the fact that every idiot on the planet thinks its supposed to work from OS X to iOS and keeps making threads and support cases for that NON feature.

I think AirDrop on iOS sucks, hopefully it won't be as half baked next time around.
 
Have you tried turning off the device itself? Airdrop did work after I did that. Also, both device should be closed to each other.
 
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