i loved Five Guys before i went gluten free and i still go on occasion. there use to be a guy at the register that was very knowledgeable and careful with GF foods, making sure everyone followed safety measures for my burger. i had absolutely no issues when he was there.
since he left, I've never had a burger turn out GF, but i still go for the fries. you can easily get enough to fill you up if you don't mind only eating potatoes. i don't know for sure if the Cajun fries are confirmed GF, but I've had them a few times with no noticeable reactions. since they only serve burgers and fries, the fryer is gluten free by default. the buns are cooked on the same surface as the rest of the burger, so that's risky despite them having a lettuce "bun". the guy at the register now doesn't seem to know anything about it.
if you go with a friend, make sure they put your food in a separate bag. last time i went, my friend's burger was dropped on top of my fries.
if you have a peanut allergy, steer clear of Five Guys, as there's a large container of unshelled peanuts for customers to take from at the front.
— Somewhat
— No gluten-free information on the menu
— Not Much
— Excellent