Your youngest is old enough, so if you are certain that you want to adopt, I would ring round every agency you could potentially adopt from. Your local authority, any neighbouring local authorities which will take adopters from your area, and any other voluntary agencies operating in your area
I do understand why Coram would be concerned about you already having 5 children and wanting to adopt a sibling group - 7 children all at home at once is a very very big task. It's hard enough with two alone, without having 5 others who all have competing needs on top of that. You may find that agencies would prefer you to just adopt the one child and then adopt again later if that goes well
Alternately, if your eldest is 15, in a few years you'll have only 4 at home.
I have known a couple of larger families adopting though so it's not impossible. I know a family who had 4 BC's aged between, I think about 21 to about 10 when they adopted (1 child). And I remember the family from 'Home for Maisie' who'd adopted a group of 2, then a group of 2, then a group of 4 then Maisie last, and certainly at least 4 of the older ones were all at home when Maisie came home
So it's not an impossible thing. However you do need to think carefully about the number of children you'd like to add to your lot, and how you would manage difficult behaviours etc as well as the strain of the move to you on everyone, and the changing dynamics of the family. It wouldn't be easy, but if it's what you want then persevere. Just because one agency won't take you on doesn't mean that every agency has the same opinion.