Has an Euros game ever ended 5-1?
Exactly once. On June 14, 2024, Germany beat Scotland 5-1, and no Euros game before or since has ended that way. When it happened it was a scorigami, the first 5-1 in league history.
That makes 5-1 the 15th most common final score out of 20 that have ever occurred in Euros. One point away, 6-1 has happened 1 times and 5-2 has happened 1 times.