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Default Count between two dates using sumproduct

Using Excel 2003, A5:A1000 is a range of dates covering 12 months, 1/1/10
through 12/31/10; E5:E1000 is a range of names, ie Smith. I need to count the
number of times Smith occurs for each month, ie January, February, etc. I
have the following formula,
{=SUMPRODUCT(--(A5:A1000=1/1/2010),--(A5:A1000<=1/31/2010),--(E5:E1000)="Smith")}, but am getting a value error. What am I missing?
 
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