Reality can trip up the most logical argument @krice118 . If the fuel pickup tube isnt all the way at the bottom or the tank shape basically allows sloshing so the pickup runs dry from time to time, you wont be able to use those 5 gallons. I thought you might have actually tested the range after the light came on.
So I was intrigued by this and recently tested fuel tank capacity by slow filling the tank. The Miles Remaining indicator showed 5 miles. The auto-stop on the gas station filler nozzle tripped at 22.5 gallons. I was able to get 26.5 gallons in there to the brim. Around town I get about 11-11.5 mpg, so with this amount of fuel I was able to go 300 miles before filling up again with 26.6 gallons.