Select the cell to colour...

Go to Format|Conditional Formatting

Select Formula is from the 1st drop down and enter formula:

=AND(TODAY()<=E10,E10<=TODAY()+5)

..replacing both E10's with actual cell address of the date. Also change the 5 (which is for 5 days out) at the end if you want to expand the date range.

Click Format and choose colour from the Font tab.

Click Ok

Clikc Ok again.