If you are writing on the Samsung Galaxy S5 text messages in the messages-app and you interrupt the writing, then you will a "draft" notice in the overview. Now, if you want to delete the draft is no this works very simply.
To do this, open the messages-app on your Samsung Galaxy S5.
If you are in the message list, tap the contact person where the draft is visible. Written text should now be in the text field of the text conversation. In order to delete the draft, tap in the text box and then remove the text with the keyboard. Is the text box blank, the additional text "draft" is automatically deleted in the message list. Finished!
You now know how to delete on the Samsung Galaxy S5 a draft in the messages-app.