Has a World Cup game ever ended 6-5?
Exactly once. On June 5, 1938, Brazil beat Poland 6-5, and no World Cup game before or since has ended that way. When it happened it was a scorigami, the first 6-5 in league history.
That makes 6-5 the 26th most common final score out of 34 that have ever occurred in World Cup. One point away, 7-5 has happened 1 times and 6-6 has happened never.