iTunes and iCloud both backup the data in your iPhone as a whole so you can only get all the data in the iPhone backup together back to your iPhone. If you want to recover deleted text messages from iPhone 5s separately, you may need third party
iPhone data recovery software. I would like to recommend
Leawo iOS Data Recovery to you because this software is helpful and easy-to-use. It is used for recovering lost files from iDevices and iTunes backups. The software also enables users to backup iPhone, iPad and iPod touch files to computer. Leawo iOS Data Recovery will export the recovered text messages to CSV and HTML files so that you can view the files with your computer.
The following guidance will show you
how to recover deleted text messages from iPhone. You are able to free download the software and have a try yourself. Note that the trial version stops at the preview window.
1. Run Leawo iOS Data Recovery on your computer, and you will see three recovery modes in the main interface, including "Recover from iOS Device", "Recover from iTunes Backup", and "Recover from iCloud Backup".
2. Choose "Recover from iOS Device", and connect iPhone to computer with the USB cable. The software will recognize your iPhone and check it at the bottom list. Click the "Start" button in the window to let the software analyze your iPhone 5s.
3. After the Analysis of the iPhone, the software will begin scanning the contents in the iPhone. When the scan is done, the names of the categories in the left sidebar will turn white. Choose "Messages" and then the contents will display in the right part of the window. Check the messages you need and then click the "Recover" button at the right bottom of the window.
4. The dialog of recovery settings pops up after clicking "Recover". Click "Open" in the dialog to choose a target folder on your computer and then click "Go" at the right bottom of the dialog.
For more methods, check:
How to Recover Deleted Text Messages from iPhone
