With C arrays, why is it the case that a[5] == 5[a] ?

The C standard defines the [] operator as follows:

a[b] == *(a + b)

Therefore a[5] will evaluate to:

*(a + 5)

and 5[a] will evaluate to:

*(5 + a)

and from elementary school math we know those are equal.

This is the direct artifact of arrays behaving as pointers, "a" is a memory address. "a[5]" is the value that's 5 elements further from "a". The address of this element is "a + 5". This is equal to offset "a" from "5" elements at the beginning of the address space (5 + a).