Given West Ham and Reading still have to play each other, I think it might be less.
If West Ham win their game in hand, we're 5 poinst clear of 3rd.
If we lost to Reading and Wham won their fixture, we're still 2 points clear of 3rd.
If we lose the fixture when Wham and Reading play each other, we're STILL in the top 2 whatever happens.
That's the worst case scenario, so if we were to win the other 6 fixtures and lose those 2, we're still guaranteed promotion.
If we beat Reading...
If Wham won their game in hand - 8 points above 3rd
Reading beat Wham (worst case scenario if we beat Royals) and we lose same weekend - 7 points clear of 3rd, equal games played.
So 5 wins (including the one against Reading) would see us up.
This assumes Reading and West Ham both win ALL the other games, as well as the above mentioned worst case scenarios.