How can you retrieve deleted text messages from iphone 5?

I suppose that you didn't backup or can't recover from iClound since you are asking the question. If that is the case, you could try a third party app like Jihosoft File Recovery. I used it to get all my data back once. Their design is good. You can have a try!

Sometimes we are just stupid enough to delete some SMS and immediately want to restore it. Or for some occasions we just tap the trash can icon accidentally and deleted all our text messages. Whatever it is the situation, retrieve lost mobile information is what we really care about. Chins up! Everything about regaining data from iOS devices, we can leave it to iPhone Data Recovery. What's that, you ask?

By using iPhone Data Recovery, your lost texts will be presented clearly back to your iPhone SE/ 6s/ 6s Plus/ 6/ 6 Plus, iPad Pro/ mini 4/ Air 2, etc. It allows you to select missing messages according to their names, phone numbers or contens. Keep rolling for more details.

See also how to erase messages from iphone in your device to know more tutorials not only about recovery but also about the deletion of files in your iPhone. This ios data eraser will delete everything from iPhone permanently including delete iphone photos, browsing history, contacts,  messages, and all contents and settings on iphone.

Yes, it is possible. Check your iTunes backup firstly, if you have sync the data from your iphone recently.

If you have neither iCloud or iTunes backup, use a data recovery tool, mobikin can help you recover deleted text messages iphone.