I teach at my dc's school.
Our next Parents' Day - which runs from 8-4.30 - happens to hit years 7,8 & 10 (previous event was for years 9,11,12 & 13 - so prioritising those with options coming up).
It so happens that I have dc in both year 8 & year 10, & teach year 10.
So I'm waiting to see how booked up I am with year 10 parents.
THEN I'll start booking consultations for my own kids around that. I doubt I'll be able to get round many. I haven't been able to make a consultation for my year 6 daughter in living memory - I'm always teaching in the Senior School when they're on!
So I ask each Head of Year to organise a quick round up by email - they do this for any parent who can't attend & requests it.
If my ds's French teacher thinks he's slacking & wants to meet, she says so. If my dd1's Science teacher wants to tell me she's outstanding, that's nice to hear.
Honestly, a 5 minute meeting is a bit pointless & outdated.
We are increasingly moving towards regular 'drop ins' - so one week it's English, say. If your kid's teacher has a concern, they invite you. If you have a concern, you rock up.
I have no idea why anyone thinks a day of rotating round 5 minute appointments twice a year is a good use of anyone's time tbh.
Anyway - I think this Head is being perfectly reasonable. If you can't fit in those hours 6 months in advance, that's exceptional circumstances & you contact the Head & it will be sorted. Sensible for parents AND for staff.