Questions & Answers about Нас было пятеро, когда к нам присоединился преподаватель.
Why is it нас было пятеро instead of мы были пять?
To say "there were X of us," Russian puts the pronoun in the Genitive case (нас) and uses a collective numeral (пятеро). Because the pronoun is in the Genitive rather than the Nominative, the past tense verb "to be" must take the default neuter singular form (было).
Could I use the regular number and say нас было пять?
You can, but нас было пятеро is the much more natural and common phrasing. Collective numerals (like двое, трое, четверо, пятеро) are strongly preferred when talking about groups of people, especially when they are the predicate to a personal pronoun like нас, вас, or их.
Why does the verb присоединился take к нам rather than just a direct object?
The verb присоединиться (to join) literally translates closer to "to attach oneself to" or "to unite with." In Russian, this idea of moving or adding towards an existing group requires the preposition к followed by the Dative case (нам).
Is there a reason преподаватель is at the very end of the sentence?