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

In practice, the difference is in the location where the preprocessor searches for the included file.

For #include <filename> the preprocessor searches in an implementation dependent manner, normally in search directories pre-designated by the compiler/IDE. This method is normally used to include standard library header files.

For #include "filename" the preprocessor searches first in the same directory as the file containing the directive, and then follows the search path used for the #include <filename> form. This method is normally used to include programmer-defined header files.

A more complete description is available in the GCC documentation on search paths.

1. A pointer can be re-assigned:

   int x = 5;
   int y = 6;
   int *p;
   p = &x;
   p = &y;
   *p = 10;
   assert(x == 5);
   assert(y == 10);
   

   A reference cannot be re-bound, and must be bound at initialization:

   int x = 5;
   int y = 6;
   int &q; // error
   int &r = x;
   

2. A pointer variable has its own identity: a distinct, visible memory address that can be taken with the unary & operator and a certain amount of space that can be measured with the sizeof operator. Using those operators on a reference returns a value corresponding to whatever the reference is bound to; the reference’s own address and size are invisible. Since the reference assumes the identity of the original variable in this way, it is convenient to think of a reference as another name for the same variable.

   int x = 0;
   int &r = x;
   int *p = &x;
   int *p2 = &r;
   
   assert(p == p2); // &x == &r
   assert(&p != &p2);
   

3. You can have arbitrarily nested pointers to pointers offering extra levels of indirection. References only offer one level of indirection.

   int x = 0;
   int y = 0;
   int *p = &x;
   int *q = &y;
   int **pp = &p;
   
   **pp = 2;
   pp = &q; // *pp is now q
   **pp = 4;
   
   assert(y == 4);
   assert(x == 2);
   

4. A pointer can be assigned nullptr, whereas a reference must be bound to an existing object. If you try hard enough, you can bind a reference to nullptr, but this is undefined and will not behave consistently.

   /* the code below is undefined; your compiler may optimise it
    * differently, emit warnings, or outright refuse to compile it */
   
   int &r = *static_cast<int *>(nullptr);
   
   // prints "null" under GCC 10
   std::cout
       << (&r != nullptr
           ? "not null" : "null")
       << std::endl;
   
   bool f(int &r) { return &r != nullptr; }
   
   // prints "not null" under GCC 10
   std::cout
       << (f(*static_cast<int *>(nullptr))
           ? "not null" : "null")
       << std::endl;
   

   You can, however, have a reference to a pointer whose value is nullptr.

5. Pointers can iterate over an array; you can use ++ to go to the next item that a pointer is pointing to, and + 4 to go to the 5th element. This is no matter what size the object is that the pointer points to.

6. A pointer needs to be dereferenced with * to access the memory location it points to, whereas a reference can be used directly. A pointer to a class/struct uses -> to access its members whereas a reference uses a ..

7. References cannot be put into an array, whereas pointers can be (Mentioned by user @litb)

8. Const references can be bound to temporaries. Pointers cannot (not without some indirection):

   const int &x = int(12); // legal C++
   int *y = &int(12); // illegal to take the address of a temporary.
   

   This makes const & more convenient to use in argument lists and so forth.