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Well the rim is something like this, which is also Hunt, although mine are hooked and a bit wider. So the well is maybe 4 mm deeper than the tyre bead seat. And if a loose tyre bead sits in that well, there will be a lot of slack: 8 mm on one side if the tyre bead was a circle.
I don't think that should affect its ability to stay on the rim once it is seated.
Tyre is a used GravelKing 38mm which seems pretty floppy as far as tyres go. Maybe that's a factor?
If it is genuinely a 5mm gap then it's never going to stay on the rim, let alone inflate. Unless you have some deeply weird rims with some obscurely cavernous central rim well.