.. I want to count the number of rows where both Column A
and Column B have a date between 01-01-05 and 12-31-05

An alternative to try, presuming data in cols A and B are all real dates:
=SUMPRODUCT((TEXT(A1:A4,"yyyy")="2005")*(TEXT(B1:B 4,"yyyy")="2005"))
Adapt the ranges to suit the actual extents. Any joy? hit the YES below
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Max
Singapore
xde
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