This is a nice combinatorics problem with a little twist. The question is asking for every combination possible that doesn't include Ben OR Ann & Ben & Ann. Rephrasing like this simplifies the problem, because we now know that out of the 7 contestants we don't want Ben or Ann to even be considered as semifinalists, so we can effectively remove them.

This leaves us with the following:
7 (starting contestants) - 2 (Ben and Ann) = 5 (remaining contestants)

Since we have 5 contestants and 4 spaces AND order doesn't matter (they are all semifinalists, aka in what order they become semifinalist doesn't affect the outcome), we can say the following:

5 choose 4 = $$\frac{5!}{\text{4!1!}}$$ = 5

Answer: A