You can save or lose a lot of money here, so play with these parameters carefully.

Where to go: US-based ethnic Indian travel agents may have a good deal to AMD itself, so check with them. If buying from "international" portals, you may be best off buying to Mumbai (BOM) and arranging domestic flights separately. (Check cleartrip.com to get an idea of BOM-AMD rupee fares.)

When: Dec 23-Jan 14 is high season, one of the worst times to find a cheap seat, especially five seats on the same flights. If you must travel on specific days you can pay a few hundred dollars per ticket, $1000-1500 extra for 5, for the privilege. Good news is, Dec 25 is usually good and there may be other holes in the tight availability. You can save money if you are flexible. As a general rule, midweek is good.

Where to buy: OK, so you need flexible date search. No US portal has it. The only good one I know of is Travelocity's Singapore portal
http://www.zuji.com.sg/web/content/sg/flights.html.
Click on the flexible date button, choose your airports as NYC and BOM (or AMD); months Dec to Jan. The very first list they throw at you is misleading: Seat availability has not been checked, fares are in Singapore dollars, and don't include taxes! Don't give up, this is still your best bet. Keep clicking until you find a fare with seats available on dates acceptable to you. Click through until you see a total fare. Multiply by 2/3 to get USD (100 SGD = 67 USD).

My guess is, a fare of 1300-1400 would be normal quote, 1200 good one, and 1000 a steal not to be missed. If you see $800, just relax, taxes will come later. Such tickets are expensive to cancel or modify, so don't buy without being sure. Once you have identified the most promising dates and airlines, you can try to buy from Travelocity's US office too, or anybody else, as you prefer.

For a thorough search, you should also check the airline's own websites as well. They often "forget" to inform outside portals of certain specials.

Also, check above mentioned "Indian" travel agencies for fares to BOM as well as any special deals to AMD itself. Sometimes airlines don't announce Dec specials until Sep-Oct, but waiting until then is risky too.

Good luck. Let us know what you find.

PS. The above mentioned Emirates 1-stop NYC-AMD at approx $1400 does seem to be convenient if nothing else. However, I realize that you are buying 5 tickets and even a modest saving per ticket would add up.

Sorry to keep on editing this, but there were many considerations here and it too a few tries.