Susan claims. "If a family has already got four boys, then the next baby is more likely to be a girl than a boy."

Assuming that for every baby the probability of being a girl or a boy is the same (50% for each of them)

We could then think in this situation as a coin flip.

Suppose that you flip a coin 4 times, and the four times you get heads.

Does this imply that in the 5th flip the probability of getting tails increments?

Well, not, each flip is an individual event, and it's outcome does not depend on the outcome of the previous flips.

The same is for the new baby, the gender does not depend on the gender of the previous babies, is an independent event, then Susan's statement is false.