Count Unique Values if Adjacent Cell is Not Blank

Ok, so here is an example of my worksheet.
Untitled.png

I am currently using the following formula to count the unique number of dates in column A (displayed in E5).
=SUMPRODUCT((A2:A5<>"")/COUNTIF(A2:A5,A2:A5&""))

I would like to make a change so the formula in E5 will only count days that have text (or are not blank) in column C of same row (so it's not counting days not worked yet).
I can't think of a good way to do this. Any ideas?

Thanks!

I thought I had it figured out, but it's having issues when there are duplicate dates and a different value in column C for each date.
I've attached an example worksheet if anyone can help.

Example.xlsx

Thanks, Tony! That seems to work.

Glenn,

The expected results for the example sheet are as follows:

If all cells in column C have values, the days worked should be 5. Each date should only be counted once, so if there are no values in C2 or C3, the result should be 4. Make sense? I was trying to use the formula in cell E6, but I couldn't figure out how to make it stop returning 0.5 for days in there twice, etc.

Thanks, all!