I know you said you don't want to go used but I think you should consider it. Have hubby go along and really put the cars through the paces of actually riding around with 4-5 kids. We have a '12 Ody which replaced an '08 Sienna and the Sienna was light years above and beyond easier for us in terms of using it with kids. I wish we had looked at a used Sienna. I was afraid to go used because our Sienna had a leak in the trunk no one could figure out and the warranty ran out and it was like throwing money in to a big leaky hole and I wanted brand new with solid warranty - did not realize that certified cars come with warranties same as new cars.
We had the 8 passenger Sienna and those are REALLY hard to find but a 7 passenger would have worked, too. When we bought the Sienna we only had 3 kids and I liked being able to have them all in one row so there would be no fighting over who got a captain's seat and who got shafted in the back row. Once we had 4, we kept 2 in the back row and two in the middle - one behind the driver and one in the center seat with the outboard seat flat for easy access to the back.
So why I hate our Odyssey. The 8th seat is better than the old Odyssey 8th seat and better than the current Sienna seat but no where near as good as the old Sienna 8th seat. It is narrow with a ceiling mounted seat belt. it is just not as comfortable as the old Sienna seat for a passenger or as friendly for car seat installs. There are a lot of seats that work but there are some that do not. IMO it's very much a last choice seat. We use it if we have a friend along but wouldn't want to use it all the time.
In the old Sienna, the outboard seats tumbled forward, totally out of the way, for easy access to the back - and then gravity would make them flop back down and lock into place if the 3rd row person forgot to do it. The Ody seats slide forward and have to be pulled or pushed at the back to lock into place - if you are driving and realize the last person to leave didn't do this you will have to pull over to fix it, you can't reach to lock the seat back into position, and it flops around while you drive. In terms of getting extra cargo room the old Sienna seats stand on end when tumbled, the ody seats have to actually be removed to be stood on end. It was really nice to have such quick and easy extra room if I was out and needed more cargo space.
The 3rd row of the old sienna was 3 - 3 1/2 inches wider than the Ody (which has the narrowest 3rd row of any minivan I think). Just a little more room for passenger comfort or car seat installation. (to be fair I think the new Ody has more leg room - so it's a toss up. Side to side room vs leg room. I am not sure I ever rode in the 3rd row of our Sienna so I can't comment - but my husband had to squeeze in back there between two car seats when we were stuck in construction traffic that was literally not moving and he had to help one of the kids use the car potty - and THEN of course we started to move again)
If you have an old 7 passenger Sienna or an old Ody (7 or 8) you can move an outboard captains chair to the center so there is a side aisle to access the back so you never have to move a seat. (although to be fair we often don't move seats in our ody because my girls who ride in the 3rd row will just hop over the center seat, which is folded flat. But they are 6. I wouldn't expect a bigger kid or adult to do that.) (And if you remove the center seat for 3rd row access, there are no inner arm rests on the captain's chairs which is a huge flaw imo. The old Ody had a narrow back and wider butt for the 8th seat so the captains chairs still had arm rests - they fit along side the back of the 8th seat. I think "wide mode" was a gimmick to allow them to keep the 8th seat small and save money while still sort of providing the benefits of a full size 8th seat)
The 3rd row windows do not open in the odyssey (new or old, unless you go really old, in which case the middle windows don't open). This really bugs me and I didn't realize it till we got it home.
The trunk in the old Sienna is slightly bigger which is a good thing with 5 kids.
Ody does not come with roof rack but old Siennas did so may be an extra expense to add. And if you add, Honda cross bars are not adjustable - not sure how much this matter but most cars do have adjustable cross bars so, just, why?
I know the new ody is a safe car and it drives great and I love my back up camera and the fuel efficiency is really good for the size - and I love the complete lack of water and mildew in my cargo area - seriously, seriously foul, we replaced the carpet twice - but in terms of fitting kids in it and getting in and out, I really miss my Sienna. Obviously this is all just one person's opinion but with 5 kids - I would look into the logistics of loading and unloading etc. You can fit 8 kids in a new Ody - but you might find the old vans' set up more convenient. OR maybe you will decide the new Ody is just fine for you.