There's no requirement in any role-playing game that I've played that every player need have there own copy of the rulebook. While it is indeed convenient to have multiple copies of books in a gaming group it is by no means a necessity.
At the table when more than one person would like to look something up, the worst inconvenience would be that people will have to wait their turn to take a look (if they're bored while waiting, they can always amuse themselves by-- oh, I don't know-- playing the game?). It can be very helpful for players to have their own books between games so they don't have to rely on borrowing the book or waiting until the next session. The best time to have multiple books would be during character creation, since everyone will be looking up rules and statistics all the time to make their characters, however during the course of the campaign I doubt there is likely to be nearly so much of a need again.
I don't think I've ever played in a game that had more than two copies of the core rules and it's never been a large issue. Most of the time there's only been one. I would suggest doing character creation and advancement as a group during normal sessions, that way the bookkeeping can be done together at once where books can be shared and no one risks forgetting to do it before the next session.
In brief: save some money and share your books. Once you're past character creation everything should be fine.
Full disclosure: I haven't played 5th edition specifically, but I've played 2nd and 3rd and from what I've heard there isn't that much that's changed to effect my basis for my answer.