I read that you stopped the mower to get a drink....so no problem there.
It restarted and you mowed 5 minutes...stopped again...sounds like a repeat(again) so what is the problem?
Did you stop or did the mower die? there is a difference.
Did you try to restart the 3rd time and it would not?
Or, there is no problem...you just noticed that there was very little gas showing in the filter (I see that a lot)
you replaced it and still there is very little gas in the filter????
Don’t know if you have a short block Chevy, in-line Ford, 383 Dodge Hemi, Briggs, Kohler or Onan. If you gave us a little more info we might be able to help. All engine number would also be a great asset to your cause.
You have got to help us...you are there...all we have is what very little you are posting....
the more info you give the more people will have to go on to help you.