Conditional Formatting 3 conditions

Hello all. I've tried to solve this by searching the forum and just can't get this right. I've attached a sample file for clarity. I would like to have 4 cells in a row react to a 5th cell in the same row. This is a job tracking file and need delivery dates watched and shaded black to orange to red as the dates get closer. I'm using conditional formatting but can't get all 3 colors to change. I'm sure I'm missing something simple but my head hurts from banging it on the wall. I need help.

Thanks in advance.

Change the conditional formatting for E3 to

Formula is =AND($E3>=3, $E3<=5)

Formula is =$E3<=2

Then copy the formatting to the other cells.

=and($e3<=5,$e3>=3)

Thanks for the catch, Martin. I corrected the earlier post.