First you'll need to make sure that the data entered in F1:F5 and A1:A20
are in the same format. Either enter true date values, which can be
formatted as you like, or format the cells as 'Text' and enter your
dates in the following manner...
0101 ---> for January 1st
and
1031 ---> for October 31st
Then, on Sheet2...
C1: Leave empty
C2: =ISNUMBER(MATCH(A2,Sheet1!$F$1:$F$5,0))
Lastly, using Advanced Filter, try the following...
1) Start from Sheet1 by clicking on the sheet tab
2) Data > Filter > Advanced Filter
Check 'Copy to another location'
List range: Sheet2!$A$1:$B$20 (which includes the header)
Criteria range: Sheet2!$C$1:$C$2
Copy to: Sheet1!$A$6
Click Ok
Hope this helps!