OK, at the risk of sounding pedantic, here goes:

In a tournament, we have a maximum number of players per group, say MAXP. We also have a number of games to be played between any two players in the group, say NUMG. Each player in the group will play all the others - the number of opponents is therefore (MAXP - 1). Multiplying this number by NUMG, we get the total number of slots needed at the most for a tournament. Of course, if a group's number of player is less than MAXP, then they will actually need less.

If anyone offers a satisfactory explanation WHY in a 5-per-group 2-game tournament one needs 10 and not 8 slots as proved above, I will have to tear up my mathematics degree, as such explanation is bound to have any number of fatal flaws...