Learn Russian: Ты работаешь в офисе пять?

When a cardinal number like пять (five) is used as a label or ID (like an office, room, or bus number), it stays in its basic dictionary form. It does not take the prepositional case ending even though офисе does.

Why is the word for office spelled офисе instead of офис?

The preposition в (in) followed by a location requires the prepositional case. To form this case for the masculine noun офис, you add the letter -е to the end.

How does Russian form a question here without using a word like 'do'?

Russian does not use helper verbs like 'do' or 'does'. To ask a yes-or-no question, you keep the exact same word order as a normal statement but raise the pitch of your voice on the key word you are asking about.

Why does the verb работать change to работаешь in this sentence?

Verbs change their endings based on who is doing the action. Because the subject is ты (informal you), you drop the -ть from the dictionary form работать and add the ending -ешь.