If you can use hotkeys rather than a button that is part of the window it's generally more reliable and easier to implement.
How often do you wish to send the control-F5 approximately? Once every 2 seconds(1/2s) .. 1/s 2/s 4/s etc..
Can you uniquely identify the window?
(Edit: ahk comes with a spy to get class name of the window etc.. but most stnadard Windows dialogs have class #32770. The class is not always unique.)
Edit2: If you don't mind clicking the window with the mouse first to make it the active window, then ID is not an issue. If the toggle hotkey is unusual then you are not likely to hit it in the wrong program. But if hotkey is OK then those details can be worked out as we go along.
And the last would be same key combination toggles on .. off or a different combo to start / stop?