Some WAPs have per-country settings, but as you say, the kit that just thinks it knows which country it is parked in may well not be alterable. Manufacturers may even release different per-country flash ROM images.
When you say your kit is ‘5 GHz’ do you mean 5 GHz-capable or 5 GHz-only?
I do have some 5 GHz-only WAPs which I am not using currently so such a thing does exist, but I have never heard of ‘client’ devices (stations) that cannot speak 2.4 GHz as 5 GHz was not that common until a few years ago and there is still a ton of 2.4 GHz-only kit out there.
Of course, locking it onto the lowest of the 5GHz channels, 36-64 fixes all problems. I am not familiar with this device but, if it is like the ZyXEL WAPs I use, then it could be that ‘auto’ means that it chooses a chooses a clear channel where there is no interference from some other access point.
With my WAPs the end result using ‘auto’ (clear channel auto-select) seems to be rather chaotic, and although it is a nice-sounding idea, it is very poorly documented and I have turned it off and fixed a channel.
I had a brief squint at the manual. I can’t see separate settings for 2.4 GHz and 5 GHz so I am wondering if there is only one radio. If so, so no simultaneous 2.4 + 5 GHz operation, and that is a bit rubbish. If that is the case, and you have no neighbours, then definitely change over to 2.4 GHz rather than 5 GHz as the range is better.
I use 2.4 GHz too with one 40 MHz wide channel there. I have two ZyXEL WAPs currently up and running, with more to be installed just sitting around in boxes. These WAPs contain two independent dual-frequency-band radios: each of which can speak either 2.4 GHz or 5 GHz regardless of what the other radio is doing, so maximum flexibility. It is not just always 2.4 GHz + 5 GHz.
One of my WAPs currently talks on 5 GHz + 2.4 GHz and the other talks on two different 5 GHz channels, all non-clashing, so that is a total of three 5 GHz channels in use each being 40 MHz wide.
I use the lowest 5 GHz channels
* 36-43 on WAP #1, radio 2 (40 MHz wide)
* 44-51 on WAP #2, radio 1 (40 MHz wide)
* 108-115 on WAP #2, radio 2 (40 MHz wide)
and
* WAP #1, radio 1 is on 2.4 GHz, 40 MHz wide
In the 2.4 GHz band, I am already hogging most of the 2.4GHz space, leaving only room for a 20 MHz channel, but that space is left free for use by bluetooth devices and so such as I have found that hogging it all causes problems with kit fighting and some non-ethernet-802.11 functions not working. Also letting such kit auto-select to a clear channel keeps it from lowering the performance of WLAN traffic by contending. I have no close neighbours, and although unfortunately a new house is due to go up, it won’t be that close and there is also my windowless, 6ft thick double stone gable-end wall acting as a massive shield blocking things in that direction. So I have all of the spectrum free of neighbours.
If your router isn't being flexible enough, then you could just get a really good WAP (or two) and deploy that instead, turning the wireless off in the original router.