iMessage has a setting whereby you can tell it to fall back to SMS if it isn't able to reach a data network or if the recipient isn't available via a data network.
This is under
Settings app > Messages > Send as SMS.
For some reason - my iPhone5 wasn't doing this. I could send iMessages fine - I could send SMS's fine - but fallback from iMessage to SMS when the recipient was unavailable - nope. It's supposed to time out and fall back after about 5 mins.
I'd tried turning
Send as SMS off and on - no help.
Then - under
Settings > Messages > Send & Receive I noticed that my phone number was listed under the "You can be reached by iMessage at:" list but not under the "Start new conversations from:" list.
It makes sense (at least to me) that a message sent from an e-mail address can't fall back to SMS - but why was the number not available? It's automatically there on the receive list and I could not see any way to add it to the send list.
So - I tried turning iMessage off and on. After about 5 mins - bingo - the number came into the "Start new conversations from:" list.
But there was a final wrinkle. Fallback to SMS would not work for any conversations already started at this point. I had to delete them in the messages app first.
Now it works - send as iMessage times out after 5 mins and it sends as an SMS.
Oh - btw - an iMessage that's waiting can be forced to an SMS - click on it and choose Send as SMS.