It should work at 5 GHz according to this https://support.sonos.com/en-us/article/supported-wifi-modes-and-security-standards-for-sonos-products

But I have put my Sonos devices on 2.4 GHz exactly for that cutting in and out as the 5 GHz signal is not so stable at my place. 
 

Are you able to configure your router? 

In the Sonos app’s Manage Networks > Networks do you have the 2.4 GHz or 5 GHz set?
 

Or do you have a single same SSID for both 2.4 GHz and 5 GHz in the router’s settings (and that is what you refer by “If I reboot the router a few times it will eventually choose 2.5 and then the speaker works fine.”)?

I have separate SSIDs for 2.4 GHz and 5 GHz. I have also reserved static IP addresses in the router’s DHCP settings for the Sonos speakers.

Note that trying to change the network in the Sonos app has not always gone smoothly for some users with the latest app. You might need to factory reset your Play:1 if you change the network (but if it currently cuts in and out then that might be the only choice). 
 

Note also that some users have recently written in forums about music cutting in and out with various services like Apple Music, Amazon Music and Spotify.

https://support.sonos.com/en/article/connect-sonos-to-a-new-router-or-wi-fi-network

I have a single SSID and not able to choose. I tries to do a factory reset with no success. As I said, as long as my router connects in 2.4 GHz, the speaker is fine. 

Seems like you may be stuck with that if you don’t have access rights to configure the router. It sounds like the 2.4 GHz would have stronger signal and would work better, and may just hope it connects on that.

Even right next to the router only the 2.4 GHz works without skipping so I don’t think it’s a signal strength issue. 

 5GHz does not penetrate walls as well as 2.4GHz.  I have a router that does what yours is doing.  It’s called band steering where the router tries to give you the best band based on, what, I don’t know.  Maybe it doesn’t work that well.

 In my previous location the router did broadcast two SSIDs with the same name:  one 2.4GHz & one 5GHz.  

I have no issues with dropouts here with the band steering, but I would prefer to have the ability to choose which band I connect a device to.  Most Sonos speakers would be 2.4GHz.

Do any of your other devices have problems with the 5 GHz? I’m thinking that it could be that the Play:1 is somehow broken or the router is broken or very picky about connection strength. 
 

My laptop and iPad would fairly often disconnect and re-connect, or data transfer would just stall, on 5 GHz even if they weren’t that far from the router. 

Do you see a difference e.g. in the (signal to noise ratio) SNR value when it’s connected to 5 GHz vs 2.4 GHz? See in the Settings > that Play:1 room > the Play:1 > Network?

https://support.sonos.com/en/article/understanding-the-network-details-section-in-the-sonos-app

Last resort would be to turn 5Ghz off.

https://support.sonos.com/en-us/article/supported-wifi-modes-and-security-standards-for-sonos-products#
 

 Not sure if this helps.