Independence of the seas has a family oceanview stateroom that can sleep up to 6 without the huge price tag.
You could look at a adjoining cabins, most ships have a few so you are just seperated by a door that would cater for your needs.
MSC and Costa do kids sail free promotions (they have to pay port taxes and flights) however they don't have that many cabins that take 5. Don't know how they work the scheme if you take adjoining cabins. However you would probably be better with RCI as they are family friendly and all the other kids are nearly all going to be English speaking. On these 2 lines, English speakers will be in the minority unless they are sailing in the Caribbean.
You also need to be careful when booking suites with RCI. I booked a suite but then found out that the 3rd & 4th beds were a double sofa bed. My children 12 & 9 didn't want to share and although the beds can be set up as singles, my husband and I didn't want the sofa bed. I changed to interconnecting prominade rooms but it cost me quite a bit more than if I had thought about this in the first place.