Uh... what?
L5 doesn't need any approval, from anybody, to put on the road in at least a dozen US states.
Right now.
If you put an L5 car on the road in Nevada next week- which you can do with no government approval at all then it's still an L5 car even if it's not approved in California.
L4 vs L5 is about capability, not legality. CAN it safely drive anywhere a human can? If yes it's L5. Those don't exist today though.
If you want that L5 car to drive into OTHER states (or countries) that do NOT allow them, that's obviously different LEGALLLY-- but that's the same as an L3 car- or an L4 car- both of which could cross state and country borders, and has nothing to do with "L5 needs government approval" and that limit doesn't make it not L5.
There's not even a government agency to approval it federally in the US for example-- NHTSA does not regulate such things at this time- leaving that regulation entirely to US states... which is WHY it's already legal in a number of them without anyone needing to "approve" it.
It's baffling this keeps coming up and keeps needing correcting-- often of and by the same folks.