Show or Hide a Shape based on where you click on the slide

Yes it's possible (though it's not something I've ever had to actually do for a client's course).

You can place a Click Box on a layer UNDERNEATH the button so that clicking anywhere other than the button will be detected by the Click Box's hit area.

You will need a User Variable that tracks the number of clicks OUTSIDE the button, and you will use this variable in a Conditional Action that is executed by the user clicking on the Click Box.  The first Decision Block of the Conditional Action will need a 'dummy condition' (such as IF 1 is equal to 1) so that its actions always get executed. It's action will be to increment the value of the User Variable.

The second Decision Block in the Conditional Action will check the current value of the User Variable and IF it is equal to 5 then one of the actions will be to SHOW the Button and another action will be to Assign the User Variable's value back to 0 again.  The ELSE action for this decision block will be to HIDE the Button.

This means that if the Button starts out on the slide as visible to the user, as soon as they click OUTSIDE the button, the action executed by the Click Box will immediately HIDE the button and start incrementing the counter.  Up until the fifth click on the Click Box nothing else happens other than incrementing the User Variable.  But then when the User Variable's value hits 5 the button gets SHOWN again and the cycle repeats.