remove scratch from iPhone 5 front glass Because I thought the gorilla glass of the iPhone 5 is pretty tuff I decided to omit a screen protection. Unfortunaltey now I have a very thin and subtle but very long (6 cm) scratch on the front glass. It is very hard to see and can only be seen at bright light and from a very specific angle and only when the display is turned off but it is still there, so ... 

I always handled the device very carefully and I have no idea where this scratch came from. I suspect the rivets near the pockets of some of my jeans.

To make sure that this is really a scratch I polished the screen with a little bit of water and a glasses cleaning cloth. The proposed scratch doesn't go away.

Is there any way to get rid of this sratch?
Yes, probably the rivets from your jeans.  I've done that before.

A screen protector is always a good idea because of the time and money involved in replacing the touch screen.  Especially for any of the iPhones; they are expensive.  I have always loved the screen protectors from Screenguardz.  Compared to the ones at Best Buy (forget which brand), they are extremely smooth and the anti-glare is great.  Here's the one for the iPhone 5...

ScreenGuardz - iPhone 5

Also, if you already have scratches in your touch screen since you didn't have a screen protector there in the first place ( duh, :D just kidding), you might check out the compound from these guys.  It looks like industrial grade stuff or something of the sort.

TDI Smart Technologies - Glass, Acrylic, and Gorilla Glass Compounds