I can't speak for the 2013 F10 M5 yet.. but being a 2010 E60 M5 driver that has literally had the car shut down at 60mph down the street from a gas station, and then rolled into one (don't forget about no power steering if this happens to you), I might be able to contribute some info:
With my E60 M5, I brought it down to "---" two days ago and filled up right after I got that "---" readout. I filled it up, and the pump read out "17.2". The fuel tank capacity for the E60 is 18.5 gallons. So I had 1.3 gallons to spare.. equals about 12mpg. I once drove (a year or so ago) with "---" for 10 miles and then filled up at a gas station.
So.. it would maybe be a fair estimate to say that once you read "---" on the F10 M5's dash (estimated 20mpg), you have about 20 miles left?