During a run in-bounds, we've got a holding call on the D. The offense accept which results in them getting a first with 5 seconds left in the second quarter. After the chains are reset and the ball is ready to play the whistle is blown and the clock started. If the period ends before the snap is taken, do we allow one untimed down or has the half ended?

You stopped the clock on the penalty, administered the penalty, reset the chains, and started the clock on the Ready for play. It's their problem they did not get the play off before time expired.

Untimed downs allow a replay when time expired on the play so that you can enforce a penalty. (How can it be a repeat of a second down when there is not time to repeat?)

Youre not going to extend the period here to get another play in

NFHS: Untimed down.

NCAA: Period over.

In FED the period cannot end if a penalty is accepted for a foul that occurred during the the last timed down of the period except for non-player or USC. In this case the foul occurred during the last timed down. Therefore, after the clock runs out, extend the half for an untimed down. Make sure you explain this to the A captain so they don't they have to rush to get the play off in the 5 seconds left. 3-3-3a

Sorry Kelvin you are dead wrong(assuming Fedrules since you make no reference.

Agreed. Fed rules definitely allow for an untimed down in this situation.

NF: The period is extended.
 

Please see case play 3.3.3 situation C. Its very close to your example.

Remember to extend the period for an untimed down when you have a PATIO:

PA Penalty is accepted for a foul that occurred during the last timed down of the period (other than a nonplayer or unsportsmanlike conduct foul).

T Touchdown. For the try.

I Inadvertent whistle.

O Offsetting penalties. Replay the down.

That's not true Kelvin, at least not under NFHS rules.

NF 3-3-3
A period must be extended by an untimed down if during the last timed down, one of the following occurs:
a. There was a foul, other than unsportsmanlike or non-player, by either team and the penalty is accepted.

It doesn't say time has to expire during the down. It says if there is a penalty during the last down of the period. In this case, there certainly was. Play the untimed down.