Count unique entries in one column where a criteria is met in another column

[DonutMonster]

Hello there,
I wonder if anyone could please assist me as I am completely stuck.
I have a worksheet of data with 6 different columns.
One of the things I wish to do is to count all the unique entries of column C when column E has a particular value.
The trouble is column C had many repeated entries - I wish to count for a particular category in column E the number of unique entries in column C.
I hope that makes sense, I've been pondering this for ages and I think I'm starting to muddle myself now. I can count using criteria, but to only count unique entries with criteria is proving a bit too tricky for me.
Many thanks for any help anyone can give.