No. Although it is plainly vegetable matter, potato doesn't count towards your 5 veg a day. I bet you aren't surprised to learn that sugar doesn't count either, even though its vegetable too. Nor bread nor breakfast cereal nor rice nor pasta, all made from vegerable matter. They all count as carbohydrate, not vegetable, for the present purposes.

At the end of the day it is advice, not something you have to do if you don't want to. If you want an unhealthy diet, that's up to you. Some people do live long on an unhealthy diet. Like Eubie Blake, a chain-smoking jazz musician who reputedly drank nothing but whisky, and who said on his 100th birthday, "If I'd known I was going to live so long, I'd have looked after myself better, dad." But statistically, he is an unusual case.