"There are a few third-party apps that have a good online reputation (some of which we've personally used): PhoneRescue by iMobie, Enigma Recovery, WonderShare Dr.Fone for iOS and Tenorshare iPhone Data Recovery are four possibilities to explore. Even after you 'delete' messages they remain on your handset until overwritten, so you should be able to recover deleted messages using these utilities - but, as we say, there are no guarantees."
Unfortunately, iCloud doesn't back up SMS in all territories, and for all phone operators. My UK O2-operated iPhone 5 falls into this category. So the following may not work (which is a shame because this is the best backup you can have for your SMS messages). You'll need only to go to step 2 to find out.
1. Login to https://icloud.com with your Apple ID and password
2. Click on Text Messages (if it isn't there your messages haven't been backed up).
3. If it is there searched the messages to find the ones you need.
4. Now go to your iPhone and choose Settings, iCloud on your iPhone.
5. Turn off Text Messages (or ensure it is turned off). I know this sounds counter intuitive but stay with it.
6. You'll see a pop-up. Select: 'Keep on My iPhone'.
7. Now turn back on text messages.
8. Tap 'Merge', and wait. After a few minutes the deleted text messages should appear back on your iPhone.