How to clear texting history on iPhone 5?

I always delete my texts and stuff, but then I noticed when I slide my home screen to the very left and get on that blank page where you can search up apps and contacts on your phone, I'll type in a word and some of my previous texts show up.
The word I type will be somewhere in the text I sent once and that's why it pops up. When I click on it (because it doesn't show the whole text) it takes me to my messages, but since that text has obviously been deleted, it just takes me to a new message page.
I really want to get rid of my previous texts and I don't know how to do it.
I have a iPhone 5!

Go on to the texting app, make sure you're on the main screen (not in a conversation - where it shows all your conversations) and on the conversation you want to delete, swipe it to the left as if you were going between screens and a delete button will appear (you may need to do it a few times if you are a bit of a novice with touch screen phones) and then click the delete button. You could also click on the edit button on the top left hand side.

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