The repeat text message alert on iPhone reminds you of unread messages based on the given interval. To disable / turn off repeat message alert on iPhone 5s, do as follows:
1. Make sure your iPhone is running the latest iOS version.
2. Open the Settings application on your iPhone
3. Open the Notifications settings
4. Under the Notification Style, find the Messages app and tap on it
5. Scroll all the way down, tap the Repeat Alerts option and make sure it is set to Never.
Tip: You may also tap the Repeat Alerts option and specify an interval to be reminded of missed messages. Available options are: Never, Once, Twice, 3, 5 and 10 times and the time interval is fixed to 2 minutes.