I believe somewhere in the rule book it states that a team "Must" start a contest with 5 players, but can finish with as few as 1 as long as they have a chance of winning...
My question is: Must a team, with 5 eligible players, play all 5? Ie. Can a coach, that only has 5 (eligible) players on the team, pull one player and play with only 4 players?
jc

No. A team that has 5 players who are eligible and physically able to play, must play 5 players. 3-1-1. 3.1.1

I suppose then, the next question would be who determines eligibility? Could a coach declare his/her own player ineligible for one of his/her own reasons? Ie. unsportsmanlike conduct.....
cl

Most likely the coach would just say that the player was hurt.

Don't know why any coach would do this, of course, I've given up trying to figure out coaches! :)

What if...
 

(Going of the deep end of hypotheticals)

The coach makes a statement that the 5th player is "hurt". Do you allow him to later enter the game?

What if.... you observed the player roll an ankle during pre-game warm-ups?

As long as you did not declare his bell rung, he can play later.

Last year I had a game with only 5 players dressed and my assistant asked if we could pull a player and go with 4 if we needed to rest somebody. I looked at him like he was crazy and the ref politely informed him that we needed to keep 5 players on the floor. I explained later to him that we could run a delay game if the players got tired. In an extreme case, I could pull a player back to only defense if I needed to to keep him rested. Never did the latter but did a lot of the former - got the W, despite losing our center with 4 minutes to play and while holding a 5 point lead. Perhaps my asst was on to something though - we ended up outscoring them while down a man!

As for injuries, it's no different than a guy coming out and returning when there are 10 players on the bench. Coach's decision as to when player is able to return to action, unless you see a concussion, safety problem or blood.