Cinco de Mayo numbers

Happy Cinco de Mayo! I'm going to coin 5 Mexican food numbers every year!

2023

1. Taco = 555^^^^^555 (Class 7: Up-arrow notation level)

2. Burrito = {555, 555, 555, 555, 555} in BEAF (Class 10: Polynomial omega level)

3. Nacho = {555, 555 [5 \ 5] 2} in BAN (Class 16: Epsilon level)

4. Enchilada = E555#{5}#####555 in Hyper-Extended Cascading-E Notation (Class 18: Bachmann's collapsing level)

5. Quesadilla = f_{ψ_0(Ω_5)}(555) in FGH with respect to Buchholz's ψ (Class 19: Higher computable level)