Strange text messages at five minute intervals with no sender
Questions for you:


Did you install an app recently? 
What app did you last install? 
How long was that going on for? 
Have you checked with your Sprint provider? You're not getting charged for those incoming messages? 


It sounds like mal-ware, but do not wish to raise alarm nor fear in you, BUT by answering my questions above to ascertain it.

Quite possibly, it sounds like a scam, if you were to reply innocently like "Who are you?" you could be charged premium rates for sending it. 

As for the gibberish, its likely in a language that is not recognized by your handset hence the font shows the "gibberish" character as a result.

IF all else fails, try a factory reset the handset at last resort.

Edit: Based on your edit, it sounds like its stopped for a good while due to perhaps its hit the threshold limit of how many SMS to be stored, then when you went to delete them, more kept coming in. 

The apps do seem legit.. btw :)

Would you not suggest try this, download this app called 'History Eraser' from Google Play, to wipe out the history of the SMS, just that specifically alone, and nothing else. See if that helps. If more are still coming in, then I hate saying this, factory reset the handset to clear out whatever it is that's causing the jam.