Stuck in boot --- Looping during booting.

Have you tried the following?

https://support.garmin.com/ms-MY/?faq=LePCURziXd4A5qZLwqKEwA&searchType=noProduct

I have tried it and I was not able to have it recognized by the Mac. My watch was off , I have pushed the action button has written, plug in the watch, launched Android File Transfer... Nothing happen.
Now it is getting harder to stop the loop. I'm obliged to push Light and Back to get out of the loop after many attemps (the HR sensor flash, the backlight goes on...)
But once off again, I have tried another time with only Garmin Express to wait for the connection. One minute pressing the Action button and... no result. The watch seems blobked on the logo until I release the action button.

During the loop sequence, now only the word Garmin appears for 1/4 of seconds unless I do the Two Beeps sequence then the Garmin title and all the small writing appears for two seconds before going into loop again and getting only the 1/4 of second Garmin title after the logo...

I don't know if I feel anger or disappointment now, certainly both. The watch will be two months old the 22nd of August old and it will need to go to Garmin customer service ? A place at 800 meters from my home by the way.
And they will refuse me to drop the watch or to pick it up once ready only relaying on a lazy courrier service (last time they took 4 attempt to give me back my 5X serviced in 6 weeks... This is really tedious.

So if you got any magical combo...

I have tried a soft reset then a factory reset: holding the start and back buttons and releasing them.

• press and release LIGHT (POWER) button, so watch enters boot sequence;
  
• when Garmin LOGO appears, press and hold START + BACK both (those two, on right side);
  
• on first beep release START;
  
• on second beep release BACK.
  
• Badaboom! (no, that's not a key ;-) ).
  

There’s one small thing that you may wish to try differently from the sequence you describe above, that may make a difference. In line with the secondary master reset described here https://support.garmin.com/en-US/?faq=wxPmdnWsev1xGRUf58oDC8&searchType=noProduct from the power off start point, you should hold ALL of the Down + Start + Back buttons, and keep them held down, as you press the Light button to start the watch into the reset sequence. After the first beep release only the Start button (so Down + Back remain depressed), then at the second beep you can release the Down and Back buttons.

The other thing I have learnt with the Fenix 3/5/5+ watches is that when they get in to this state it can take up to 30 minutes for the watch to reboot after a secondary master reset; so do give it time to do it’s thing (more so if you have formatted the device, as I once had to do with my Fenix 5 to clear a corrupt file - I don’t suggest you do that with a 5+ though as you’ll at best loose the maps on the watch).

Thank you for the link (I'll keep it) and the tips. Unfortunately they came to late.

Because this morning after opening a ticket, I've had the rare opportunity to meet a Garmin tech today.
Actually I felt like going to the vet: can you do something doc ?
But he has tried everything (even some custom homemade programs) to relive my Fenix 5X Plus.
In vain.
He has kept mine and he told me that Garmin will provide a new unit and he will speed the process to ease the frustration.

Kudos for Garmin France customer service, great people !

So beware the beta 3.55 as it is the only update mine got before its death.

Excellent customer service at Garmin France.
They have managed to exchange it today!

The adventure continues.