Failure to load pics from messages sent to me on my iPhone 5.

If the picture were sent to your by MMS system, the problem should be your carrier, try to call them to know more, you can also check the Message options on Settings to know if "MMS" is set as "On" to be able to send and receive pictures from SMS and Text from your carrier...
But if the service it's from iMessage, check your Internet conection to know more..
I almost forget to tell you to check the storage of your iPhone too, if a picture it's a High Resolution you'll need more free space on your iPhone to load it!

SMS (Short Message System) you can sent only text by this method, pictures and videos cannot be sent by this system, if your carrier charges you by messages, it's great to know how big the message is, more expansive it will become, a simple SMS have only 160 characters (letters and spaces), if you pass this number, you'll be charged for another message and this way continuing the value

MMS settings are for Multimedia Message System.
You can send Pictures and in some cases Video and audio (some audio are not available on iPhones).

It's a total diferent way to receive and send MMS from SMS, because has a different setting, it use a Multimedia account on your settings...
All iPhones have the MMS and SMS settings automatically on the process you put the SIM card.

My image do not show up in my text m

Please don't post the same question twice, it makes it difficult for people to help you and for you to keep up with multiple posts about the same subjecdt.