It's likely she either heard "fat" used as a taunt in the playground or has overheard adults discussing diets or weight issues.
Wherever she got the idea from, be brisk and no nonsense about it. At her age I'd be more concerned with name calling than the possibility of later eating issues. Like dealing with swearing, sometimes it's better not to show huge angst at something children say, or they'll see it provokes a reaction and repeat it. If she keeps on, reassure her as you already have done, she's not fat you are taking care of her and that means making sure she's eating sensibly and brushing teeth etc etc, all part of growing up. Hopefully at 5 she'll be happy with that and let it drop.
When looking at family photos of different people, different ages, different sizes, or people in magazines, you could casually point out to her there's a whole variety of body shapes and sizes.
I never went in for cajoling the children to clear their plates, if they had eaten a reasonable amount and were full that was enough.
When my DCs were in their early teens, I realised my DS was calling his younger sister fat one day, (she's never been), just to wind her up. I jumped on that straight away. Hitting puberty there will be natural body changes and neither girls nor boys should see this as anything but normal and acceptable.
Should say, heard somebody tell off their OH once for tickling their infant DD and singing "Hey fatty bum, bum, sweet sugar dumping". She said it would give their child a complex