One column in my spreadsheet contains dates in the format mm/dd/yyyy.
Many of the cells in this column are blank, but for those that contain
a date, I want to determine which ones come after 05/13/2007.

I have created a column next to the date column, in which I hoped to
put an X in each cell that neighbors a date after 5/13/2007. I have
tried to use the formula
=IF(AND(cell=DATE(2007,5,13),cell<=DATE(2007,7,5) ),"X","O") ... As
this has worked for me in the past. In this case, though, it is
putting an O in every cell regardless of what the date is.

Is there a better formula that I can use?

Might there be a reason that this worked on other spreadsheets, but
not on this one?