It happens only on "screen 2" and it doesn't matter which physical monitor I have selected as screen 2, it only happens on screen 2.
Normally one would thing horizontal or vertical refresh rates but you're kinda special with it on which ever monitor is #2.
go straight DVI to DVI and get rid of the conversion from HDMI.
and does that second monitor have anything other than analog to connect to? If you can temporarily borrow another monitor or use your TV, see if it still happens connected to them preferably using digital signals.
The 5450 is getting long on the tooth too. Maybe it's faltering. A nice shiny R7 xxx might be a worthy replacement.