Using SUMPRODUCT with COUNTIFS criteria? Other Options?

[CrocHntr]

Hi,

I've tried to research the SUMPRODUCT and COUNTIFS answers on the board, but just can't seem to find a solution that fits my needs (or I can't seem to apply it at least )

I've attached a spreadsheet with a sample of data. Typically my data size will be 10k+ lines, so I desperately need some kind of calc to help me with the solution.

What I'm trying to do is to count the unique work orders in Column A based on specific criteria in columns B-E. The columns look like this:

sampleexercise.JPG

My criteria may vary, but for this exercise I'm looking for Date Between 8/26 and 8/30, W/O Type = "IN", Bill Type Code = "S", and Emp Type = "GZ". I believe the answer should be 2 in the screenshot sample (or 4 in the slightly larger attachment)

I don't want to use a pivot table or filter because I'm going to eventually have the spreadsheet locked down so users can only paste in source data and then print the summarized invoice. So hopefully there's some kind of formula I can use...

Thanks for your help!