The alcohol shown ionises (loss of hydroxide) to give a carbocation. Counting each carbon atom separately, how many carbon atoms carry the positive charge in at least one resonance contributor of this cation?

The alcohol shown is 1-phenylprop-2-en-1-ol and gives the 1-phenylallyl (cinnamyl-type) cation. The charge is on the benzylic carbon, on the terminal CH2 through the allyl shift, and on the two ortho and one para ring carbons. That gives 1 + 1 + 3 = 5 (checked with RDKit).