Go straight to filling station and put at least 10litres in. An indicated 5k is not much more than vapour.....
I think most have a 'reserve' amount after that, as its very likely that the sensors cannot know how much is exactly in the tank as most are odd shapes.
My Mazda3's low fuel' warning light comes on when it has (according to the handbook, if I recall correctly) about 35-50 miles of fuel left on the fuel computer and nearer to twice that in reality (depending on driving style/location); similarly for my previous car, a 1996 Micra.
Needless to say I did test this to the limit in the Micra once (I forgot the light was on from my morning commute [35 miles each way]) and ran out of fuel (I would say at 60 miles after the light came on) in the fast lane of the A1!! I just made it over to the slow lane, but still had to push it (fortunately on a down slope) 100m to a small exit (no hard shoulder) just south of the M25 junction in the dark/rain! I had to phone my Dad to buy a petrol can and some fuel and bring it to me - I'm sure you can appreciate the look on his face when he arrived! NEVER AGAIN.
Its just not worth it to keep going - but best to keep an eye so that you don't get low on fuel when you're on the motorway (forgetting the possibility that you could run out due to traffic) - more to do with the extortionate prices filling stations charge in such locations. I find it best to make sure you know of some cheaper filling stations (locally or on the way/at your destination) via PetrolPrices or similar to get the best deal. It can make a large difference over a year.
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