power 5v with 6v (4x1.5v batteries)
You are basically asking whether it is OK to apply 6 V power to a particular board.

That answer can only come from something called a datasheet.  Look on the web site of the board manufacturer, and go back to whoever sold you the board.  One or the other should supply you with, or give you a link to, this datasheet.

The datasheet is a collection of specifications.  There will be two relevant ones to this question.  One will be the Absolute Maximum power voltage.  That's what you can't exceed and still expect the board to function afterwards.  The other will be the Maximum Operating voltage.  That's the maximum you can give it while running and for it to still work correctly.