Firstly the fact that the matches are drawn between rounds as opposed to the entire draw being set at the start of the tournament is immaterial. To reach the final, team 5 needs to be the highest ranked team on their side of the draw.

So the chance that the other seven teams in the same side of the draw are ranked lower than fifth is:

11/15*10/14*9/13*8/12*7/11*6/10*5/9

This cancels down neatly to 2/39, which is just over 5%.

Alternatively, you could ensure that the best four teams are all in the other side of the draw to team 5:

8/15*7/14*6/13*5/12

Which again cancels down to 2/39.