How to get my iPhone iMessages and text messages to delete?

I have the iPhone 5S, with the most recent update. I don't delete my text or IMessages, so my phone has a lot of them. I've been trying to delete them by sliding the message then selecting delete. They will temporary delete, but it won't let me click on any messages after i have deleted some of them. I restart my phone, and when i turn my phone back on and click on messages all of the messages a previously deleted are back. How do I get rid of them without them coming back?

Try deleting the whole conversation