10 matches.
Player A, B, C, D, E
A-B, A-C, A-D, A-E
B-C, B-D, B-E
C-D, C-E
D-E
This is one match each per person.
A-B in first match. So if you go to B bracket. He can't play A again, so A is not included. And naturally he cannot play himself. B-B cannot happen. So you start as B-C.