Like in the headline mentioned I get a token Mismatch Exception if I try to do ajax request. 
The strange this is, I do have the csrf_token in my code.
In my <head> ... </head> i have added this line: <meta name="csrf-token" content="{{ csrf_token() }}">
And above the ajax code I've got this code:
$.ajaxSetup({
    headers: {
        'X-CSRF-TOKEN': $('meta[name="csrf-token"]').attr('content')
    }
});
But I also tried to put the code into my ajax code. Like this:
        $.ajax({
                type: "post",
                url: "/sendAnswer",
                headers: {'X-CSRF-TOKEN': $('meta[name="csrf-token"]').attr('content')},
                data: {'question': question, 'answer': answer},
                success: function (data) {
                },
                error: function (data) {
                }
        });
And I also tried this:
$.ajax({
        type: "post",
        url: "/sendAnswer",
        data: {'_token': "{{ csrf_token() }}", 'question': question, 'answer': answer},
        success: function (data) {
        },
        error: function (data) {
        }
});
Now everything I've tried, gave me a Token Mismatch Exception back.
The Javascript code you see is at the very bottom of my page.