Hi Gina,
There is a
Walt Disney World Special Offer explained on the Disney website for Military personnel and families. This available through your participating U.S. Military Base ticket office.
With this deal, it says that no more than twelve 4-day Military Promotional Tickets may be purchased, activated, and/or used by any Eligible Service Member or spouse during the life of this promotion, and no Eligible Service Member or spouse may purchase, activate and/or use more than six (6) Disney 4-Day Military Promotional Tickets during any single week of the promotion.
There are some additional rules that apply, so I encourage you to go to the above link to make sure you read through them carefully.
Generally, however, you are correct in that there is a limit to a purchase of 5 military discount tickets per family through Shades of Green. However, they do allow exceptions for larger families.
There is no military meal plan available. In order to qualify for the Disney Dining Plan special free offer, you would have to purchase the package at full price.
Thank you, and I hope you have a wonderful time at Walt Disney World!