First Part
=IF(E1>0,"GREEN",IF(F1<=TODAY(),"RED",IF(F1<=TODAY()+5,"YELLOW",IF(F1<=TODAY()+365,"WHITE","GREEN")))) will set the text, then use conditional formating for the column to identify the "RED", "YELLOW" and "GREEN" components, the cell should be formatted as WHITE already, the last "GREEN" in the statement could be anything you want.
Should also mention adjust references as necessary, the first part of the statement allows any value, so even if you don't enter a date but mark it as complete it will still work.
IF statments rely on finding the first 'TRUE' value, all the rest are then disregarded
Bookmarks