For the record, I do have a FIve Guys a few miles from me, and have eaten there. I just haven't taken the shop since they came to CA. I took a Five Guys shop many years ago when I was on a hotel assignment in Atlanta and wanted an excuse to try it, but that was back before I was keeping good records and the computer I had back then has long since passed away.
While I was being facetious about being able to eat a different burger each day of the year, I definitely could eat a different one every day for a month without leaving my neighborhood....and I know of some others that are shopped.
Just within a few miles me, in addition to the ones I have mentioned above, there is:
-Wayback Burger
-Fatburger
-Twin Sliders
-The Counter (I forgot that I used to shop that one too)
-25 Degrees (this is a gourmet burger joint in the Roosevelt Hotel)
-Fat Sals
-Mo Better Burgers
-Cassell's Hamburgers (another L.A. favorite)
-Dog Haus (also shopped. Mostly dogs but they serve burgers)
-The Original Ramen Burger (with a bun made from ramen noodles, in Koreatown)
-Butchers & Barbers (A gastropub with an amazing burger)
-Belcampo Meat Co. (This is a butcher and grill. There are a few locations and people wait up to an hour for a seat to get a burger there)
-Tommy's Original (the classic chili-burger)
-Stout
-The Burger Factory
-Kitchen 24 (I've actually shopped this burger but it didn't make my favorites list)
-Astro Burger
Elsewhere in LA we have a few other famous burger joints, namely:
-Fathers Office (A beer pub with an amazing burger)
-The Apple Pan (An old-school diner with the original favorite burger of L.A.)
Not mention a plethora of Burger King, McDonalds, Johnny Rockets, Cafe 50's, Jack in the Box (have also shopped that one), Wendy's, and Carl's Jr. throughout the city.
Lot of burger options in L.A. That's 32 listed so far within walking distance of my home and I'm sure there are many more.