Is it a school with initials AG?
If so, then it had 855 in Jan 2024, not 853, and 119 of those were in the sixth form, so there were 736 in the rest of the school. They will put the updated numbers in their case.
Their PAN was 145 in the determined 2025 admissions policy, and their year 12 PAN was 150.
If they admitted 150 in year 7 then that is 5 over PAN and they presumably have 5 full forms of 30.
They may have capacity in their sixth form, and possibly in some other year groups. However, the only thing that matters to your child is whether year 7 is full.
If their entire case is built around overcrowding in corridors then you can knock it down, but it is more likely to be based on having 5 full classes.
If it's not in their case already, the panel will probably ask the admissions authority rep what the classroom capacity is, and how many adults are in the room (more space may be needed for teaching assistants, wheelchairs etc). However, the basic case will be teacher-student ratio - anything over 30 is very unreasonable, and even 30 is well above average for a secondary school (they need spare capacity to accommodate options groups, low attainment groups etc, so tend to keep numbers lower than 30 unless really struggling for budget).
However, you may get lucky - concentrate on strengthening your own case. The school's case will probably be heard at a group hearing. If the panel decide they can admit one or two, your case will need to beat all the others.