It’s not grammatically incorrect, but using on twice in that first sentence makes the sentence rather clunky. That’s why I changed the first on to aboard (which sounds more nautical anyway).
The first word of the third sentence needs to be capitalized.
I changed the comma after PA system to a period because what precedes it works better as an associated action (some people call these “beats”) than as a dialogue tag.
The captain’s dialogue contains a comma splice. Change the comma after fallen to a period.
It’s pushing the limit of how large an exact (instead of rounded-off) number can be and still be spelled out instead of written as a numeral, but the number of remaining passengers does need to be expressed with words: five thousand, one hundred thirty-two, not 5,132.
You’ll also notice that I broke this example up into smaller paragraphs. A new paragraph should be started each time a new speaker is introduced or when, as some advice expresses it, “the camera moves.”
Someone is murdered aboard the cruise ship you’re on. Passengers are told to lock themselves in their cabins and await instructions.
The captain speaks from the ship’s PA system. “The first contestant has fallen. Only five thousand, one hundred thirty-two remain.”
With that, the doors all click and swing open.