Unfortunately, trying to book 5 person rooms without talking to a person is really hard.
NCL and Carnival will let you do it on the site, but others like RCL require that you call.
I ended up booking connecting ocean view rooms on Carnival, which was much cheaper than any of the suites while affording us more room and a second bathroom. Our kids will be 6 at the time of sailing, so we didn't want the balcony, but they were available connecting as well.
A call to a TA or the cruise line is the easiest way to do this, as they can look up which connecting rooms are available that meet your party size. You can also start the process of booking the first room, looking at all the rooms still available with connections, then seeing if any of them connect to another room with the correct party size (Carnival had a lot of 2s that connect to 2s or 3s that connect to 3s, which we couldn't book). This is super time intensive and annoying, though.