The fact that the bet specifically says "In 5 years..." at the beginning and the OP is trying to redeem it now gives context as to approximately when the bet was made, even without a specific date.
Of course, I have no idea how Finnish law works, but that just seems like common sense.
Law is pretty simple in this case, the debt is overdue as he hasn't reminded on time. If it was mentioned by the OP to the other party after the 5 years, the debt is valid still. Just a mention of "hey you remember the beer you owe" makes it legally binding. If he didn't mention it, like in this case I think he didn't, the debt is no longer in effect.
Case of the other party being drunk and the debt being made at 3am don't have effect, if the OP (and in this case it's even in writing) has understood the promise.
Edit: Let's say the debt was written 11 years ago, so it was due 6 years ago, so the debt would be old after 3 years, if no mentions. If OP mentioned it however, that extends it another 3 years. so it could be still in effect today, as this thread, if the other party is aware of it, can be deemed as a reminder.
In my previous reply I hadn't seen the image for some reason.
Edit2: Applicable law is 2003/728 §5, 10 and 13a