For those who couldn't follow Siegmund's excellent response:

Because you're choosing five cards out of 7. All one pair hands are also a high card hand, because you can choose a different card to the pairing one. Same for some flushes, straights, and two pair hands.

So the actual number of high card hands possible when choosing 5 cards out of 7 is far higher than any other combination. The number quoted above is the number of hands which can't make any other combination except high card.