When I change background on my desktop, it changes my laptop

Hi Asalz
 
Welcome to the Community Forums.
 
As far as I am aware the answer is 'No'. Whilst your subscription covers 5 devices the installation of WSA on each device is discrete, i.e., it only works/impacts the device it is installed on.
 
The online console (HERE) on the other hand allows you from the web to control aspects of WSA's behaviour on each device cenbtrally...but not the Desktop background.
 
Regards, Baldrick

? Are you using Windows 10 and logging on to Windows using a Microsoft account? if you are and in All Settings Synch your settings under Accounts is set to on then your Desktop wallpaper will be the same on all your PCs.

Alternatively, if running Window  8.1, it could be due to your OneDrive settings, if you use OneDrive, that is.
 
If you do then once signed into Windows using our Microsoft account, access the Charms bar. Click on 'Settings' followed by 'Change PC Settings', click the OneDrive link to the left hand side of the screen and then click Sync settings.
 
Look in the 'Personalization' settings section and change the switch labelled 'Appearance' to the 'Off' position. If  this was in the 'On' position then doing this will stop your desktop background, colors, lock screen and account picture from syncing across devices.
 
Regards, Baldrick

Thanks for the extra information, Baldrick, I couldn't remember whether the same thing happened on Windows 8.1,;)

No worries, Sheltieuk...I suspect that the same will be the case of under Windows 10...will be interesting to see if the OP responds and what transpires. ;)