You need to do some detective work because your replies don't show the timeline of changes made before the issue occurred.
1) This has happened in the last few days. Each stroke takes many seconds to show the change on the screen, circles stay when the curser should appear and then the cursor finally returns.
2) Do not know what to check to see if settings have changed since upgrading to 5.4LR. Computer is new, image resolution is raw, Camera is Nikon D4. Have not had any problems with any of these only since Friday.
3) It was happening in 5.3 as well but I shall try to downgrade and see what happens.
So what did you change and in what order just prior to noticing the sluggish brush behavior (LR5.3>5.4 Update (New Computer added, Other changes)? If LR5.3 was working without issue on the new computer then perhaps something with the LR5.4 upgrade has caused the problem.
SUGGESTIONS
1) Backup your LR5.4 catalog and makes sure 'Test integrity' and Optimize Catalog' are checked.
2) Close all applications, shutdown your system, and power off ALL connected devices and the system. Wait 30 seconds. Power up all devices, restart, and try again.
3) If the issue persists try deleting your LR5.4 Preferences file:
4) if still no joy uninstall LR5.4 and the LR5.4 Preferences file. Reinstall LR5.3.