We are a family of 5 as well, and were on a VERY tight budget last year when my MIL and FIL paid for a surprise trip to WDW for all of us, airfare included

. We were so limited that we told the kids upfront that we wouldn't be buying things from the parks, beyond a lanyard each and one pin from each park for the lanyard. They had brought some money from their accounts, $25 each, and that was to buy one bigger souvineer near the end of the week. We also told them ahead of time that we wouldn't be buying lots of treats and such, we just didn't have the $$, and thankfully we were on the DDP. We probably spent around $250 for the 5 days, DH and I bought nothing, the kids just the pins and lanyards, and a couple breakfast items OOP. I had gone to the dollar store before we left and bought everything disney I could find, spent about $20 and got them each an autograph book and matching pens, a bunch of pins that flash, a bunch of glow sticks, stickers and little notepads, etc.....and also I had gone to
walmart and got them each a disney t-shirt which we surprised them with on the first day so they could wear to the park. It worked out really well, they did not bug us for things AT ALL, and we were very relieved to not overspend. This year we are in a much much better place, and will not be so limited, but I still plan to visit the dollar store and walmart for some pre-shopping, because things there were $$$. One thing I will not do this year is be so hungry all the time. Even tho we were on the DDP, there were still lots of times last year when DH and I were hungry, but just couldn't bring ourselves to pay the high food prices, ended up eating a LOT of squished flat granola bars (developed a real aversion to nutra grain bars which I still can't get past, they wil forever be associated with being starving at Disney

)....
Anyway, this year the trip is already totally paid for, and we are $900 ahead, so I think I will be much less worried about money, and have a better time.
Anyway, the point being, that a family of 5 can make out OK on $250, but more realistically, $500-$1000 might be a better amount to ensure an enjoyable vacation for all.