You can try using Countif():
If you want your dates hard-coded in the formula:
e.g.
=COUNTIF($B$2:$B$10,">7/30/2006")-COUNTIF($B$2:$B$10,">=8/5/2006")
If you want to reference dates in cells
e.g
=COUNTIF($B$2:$B$10,">"&G5)-COUNTIF($B$2:$B$10,">="&G6)
Where B2:B10 house the Hire Dates
G5 and G6 hire reference start & end dates.