I think this might be helpful.
=DATE(2015, 5, 20) - returns a serial number corresponding to 20-May-2015.
=DATE(YEAR(TODAY()), MONTH(TODAY()), 1) - returns the first day of the current year and month.
=DATE(2015, 5, 20)-5 - subtracts 5 days from May 20, 2015.
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