Is it okay for a professor to leave the classroom only 5 min past the class start if nobody has shown up?

I think this is less about regulations and more about respect and conditioning the students. Also, don't feel offended, you are not the (primary) reason for what happened.

Legitimate Reasons for Leaving

Respect

The fact that 0% of the students arrived shows the professor an

• immense lack of interest in his teaching subject ("I disdain the subject that you spend years researching and thus I disdain you.")
• OR complete disregard of his didactic skills ("You are so bad at teaching, that I don't think I can gain anything from your lecture.")
• OR disregard of his personal status ("You are such an unimportant person and your status is so much below me, that you will have to adjust your life to mine and wait for my arrival.")

Even if the class only consists of 5 students, he might extrapolate that everyone has one or more of these convictions. If he waits for students to arrive, he accepts his lower status and/or personal offense.

Operant Conditioning

If the professor waits for students to arrive, they will be conditioned that coming late has no negative consequences. Canceling the class will incur a penalty to students and might force them to take arrival times more serious in order to gain the advantage of having the course material explained to them.

Recommendation

Communicate (in person or via e-mail) to the professor

1. that you are very sorry for your absence
2. state your reasons (should be severe enough)
3. and make sure to allude to one more of the three points mentioned in the respect section.

If he feels that you have legitimate reasons for being late and that your absence was not a sign of disrespect, I am sure that he will be more inclined to wait longer next time you are late or might even offer you to come by his office to "pick him up" for the lecture.

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OP's Update

(This should probably be a new question, since the update significantly changes the circumstances.)

I am very sorry that the professor refused to give a lecture for you alone. It is not your fault that you were the only present and thus it is imho unfair that you have to bear the consequences.

Updated Recommendation

I would approach him again

1. start with how unsatisfactory the situation for him and you is
   • again alluding to the respect section and
2. then ask him: Why do I have to bear the consequences for the action of other students? hoping that he is rational enough to realize his mistake. Basically you should try to make him understand that he does the same to you that other students are doing to him.

Maybe he was just disappointed about the low presence again and is an overly emotional person. Unfortunately that is not something you will be able to change.

If this does not resolve the situation I would ask around the department for existing regulations regarding this.

If my classroom was empty a full five minutes after class was scheduled to begin, I might start wondering if, unbeknownst to me, class had been cancelled for some reason. I don’t know that I’d leave after a mere five minutes, but I would certainly start thinking about it by then.

To prevent this from happening again, perhaps the best solution is to make sure at least one student is on time – even if you all have to draw straws to figure out who that will be.

There is really too little information provided to say much else. You have omitted a lot of critical details, such as the size of the class, how bad the weather was that day, and how habitually students wander in late to class. If the majority of the class is rarely on time, your professor might have been using this as a chance to teach a lesson about promptness, manners, and the value of an education.

Generally, Professors have the authority to schedule their classes as they see fit in accordance to their department policies, i.e. tests and assignments. Ultimately, cancelling class is usually at the discretion of the Professor in question.

If you are concerned with missing out on class materials taught on that day, or if attendance is part of your grade, it would be wise to send an email to the professor indicating that you were present on that date (albeit late due to the subway delay) and that there was no one present in class.