Learn Russian: Без пяти два они читали объявление об отправлении рейса. - At five to two, they were reading the announcement about the flight's departure.

When expressing "minutes to the hour" using без (literally "without"), you never use the preposition в. The phrase без пяти два works perfectly on its own to mean both "it is five to two" and "at five to two".

Why is пять changed to пяти, but два stays in its normal dictionary form?

The preposition без always requires the genitive case, so the number of minutes (пять) changes to пяти. The upcoming hour (два) stays in the nominative case. You can translate it literally in your head as "without five (minutes), the hour is two."

Why does the sentence use об instead of о before отправлении?

Just like "a" becomes "an" before a vowel in English, the preposition о (about) becomes об when the next word starts with a vowel sound. Since отправлении starts with the vowel "о", we use об to make the phrase flow better when spoken.

Why is рейс (flight) written as рейса at the end of the sentence?

It is in the genitive case because it means "of the flight" (the departure of the flight). In Russian, when one noun belongs to or modifies another like this, the second noun takes the genitive case.