Can I mark sms as read in the notification menu? When get an incoming sms and view it in the notification menu (swiping down from the top of the screen) I can sometimes read the entire message there and I don't need to reply to it. Is it possible to mark it as read there and then? The two options I have right now is "reply" and "call".

I am using a Samsung Galaxy S5 with android 4.2.2
Yes indeed you can! It's not a 'stock' or 'Hangouts' feature though, but there are apps that can perform this functionality. 

 SMS notifier on the  Google Play store has this option as you will see in the screenshots for it. 

Off the record a friend said that Google tend to prefer you to Activate something, rather than mark as read! That's why you don't see this option very much. 

As per bmdixon: This does not work in Hangouts. It seems OK if hangouts is not the default SMS application, but this may vary between Android Versions and OEM devices.