I would say don't tell them yet. Find out if you actually have a problem first. Speak to the official persons involved with the collection of the papers and ask if they paper has been accepted. If yes, then you have no problem.
If no, then explain why you were 5-minutes late and be honest and say how you got your timing slightly wrong, had some problems with the printing of the paper and how you hope that they will be understanding. You can say that you feel very stressed because other people depend upon the result and that you don't want to let them down.
You didn't make a huge error and most people respond well to a heartfelt and honest plea for understanding.
If this doesn't succeed then you must accept responsibility for the consequences of a tardy submission. You can explain to the group, along with all ideas you have for getting a solution - such as writing a letter to the relevant head authority or whatever else you think might work.
Don't give your friends things to worry about and to feel bad towards you about until you know the full situation and have some possible solutions worked out.
I hope that this helps you.
Nick Nick Pagan