Your code:

    int a = 5;
    int b = a++;

has well defined behavior. The first line initializes a to 5. The second initializes b to 5 and sets a to 6. (The language doesn't specify the order of the two operations of assigning a value to be and incrementing a, but in this case it doesn't matter.)

Giving 13 for a++ + ++a is not a bug in the compiler. It's a bug in the code.

The correct answer to "what does a++ + ++a do" is "it gets rejected in code review and replaced with code that expresses the actual intent.