Yes, a family of 5 can stay in any of the 3 hotels in a standard room. I sometimes get sites that won't allow me to book it that way, but it is that site's rule and not the hotel's.
Try other booking sites besides Disney (Getawaytoday, Expedia, Travelocity, Orbitz etc) to check availability. You can usually find it on at least one of them. If they won't let you book as a family of 5 on their site, just put in 4. As I said, the hotel allows 5 per room so you wouldn't be breaking any resort rules. Oops--just realized you probably need to book it as 5 so you all get the 5 for 3 hoppers.
You can also try calling the hotel directly. If they don't have availablity, call back every day and keep asking because people cancel all the time.
One tactic I had to resort to last year was to break the trip up into smaller chunks and then combine them once I was able to get all of the nights I wanted. If any of the nights you request is booked, for example, they won't tell you (in my experience) that it's only one night that's unavailable, they'll simply say that your 5 nights are not available. If you can book, say, 3 or 4 of the nights, there is an excellent chance that the other(s) will eventually open up. It's kind of a pain to do it that way and I'd only choose this option as a last resort but it has worked for me. You do have to find CMs that will then roll it into 1 vacation and give you the promo. If you get a CM that is unable/unwilling/uninformed about doing that, just call back until you find someone who can do it. If you find it necessary (as I did) to have more than one reservation before you could combine them into 1, you will need to pay a deposit on each one.