If you send a text message with your Samsung Galaxy S5, it may happen that this remains stuck in the Outbox and is not sent. Usually this problem can be fixed with one of the following approaches:
First: Restart your Samsung Galaxy S5 to ensure that all errors are excluded, which are caused by a SystemApp that does not work correctly. In general, the SMS sending works then again as usual.
Second: Verify with your Samsung Galaxy S5 that the correct number is entered in the message center. To check this, please proceed as follows on your Samsung Galaxy S5:
Open from the home screen:
Menu --> Settings --> Section "Applications" --> messages --> text messages
In this menu you can now see the message center. Tap the entry and check whether the number for your provider is correct:
Message center numbers for United Kingdom carrier
Tesco Mobile: +447802092035
Message center numbers for USA carrier
If there is now number defined, then enter the number for the message center as above listed. You should then be able to send text messages with your Samsung Galaxy S5.