That's almost certainly a defective monitor profile. Seems the Spyder isn't performing as it should. This often affects different apps in different ways.
Just as a test, try to replace the Spyder profile with sRGB IEC61966-2.1. If this makes the difference go away, that's confirmation that it is indeed a profile problem. Remember to relaunch both applications when done - they both need to load the profile at startup.
Don't change anything in Color Settings - that's not where the problem is. Any document profile should always display correctly, whatever it is.
Thanks for taking the time to reply. I've made the changes as you have recommended and the problem persists. Any ideas where to now?
is it worth reinstalling the colour profiles or Spyder5?
Hm, OK. But this still has to be in the display color management chain somewhere.
Are you using a dual/multi-display setup? There have been instances where one app uses the wrong display profile - it uses the profile for the main screen even when the application is on the secondary screen. So the wrong numbers are sent to the display.
Next, take the GPU out of the equation. In Photoshop, display color management is handled by the GPU in "normal" and "advanced" mode. In "basic" mode it's done by the CPU the traditional way. Anyway - uncheck GPU altogether, in both apps, to be sure.
Also try to use some other document profile, just to rule out a corrupt one. Lightroom uses gamma 1.0 ProPhoto internally and you can't change that. But try to set Adobe RGB or sRGB in Lr External Editing - this profile will be preserved and used in Photoshop. No need to change the working space in Photoshop.
So I formatted my pc in the hophope t it will fix the problem. I calibrated my screen and actiactived the profile. The problem has reappeared in photoshop but goes away in Adobe rgb 1998
I should say editting in Adobe rgb colour space. Sorry for the typos my phone is playing up