I agree with you that this is unfair.  It is unfair to you and to her.  It would be best if the school could make an exception due to your circumstances, if you can explain it well enough to them.  However this is not always the case.  If you cannot get the rules bent so that your daughter does not get punished for the situation, then the next best step might be to help her realize that it is not really punishment, but an unfortunate situation for her.  Explain to her that you understand her pain and wish you could fix it for her.  Try to help her make the best of the circumstances.  If she likes to read, then this may be time for her to read her favorite book, or to work on homework, so that she can have more time to play after school.  It's a cliche, but look for the silver lining.  Turn this problem into an excellent learning experience for her.  And try back periodically to talk to the school about the situation and ask that they reconsider.  I wish you luck.

Nicolek,
Is this something that has happened more than once?  Like the other commenter said, it might need to bring up to the school about your circumstance.  Be sure to remember, however, that school is very important and they will probably not change the rules for one person.  School is important, even those five minutes that she is missing.  There are morning announcements, and just getting started for the day.  Good luck, and I hope everything works out!