5 a day is where it is recommended that you should eat 5 servings of fruits and vegetables every day, similar to 'an apple a day keeps the doctor away'.
Most things count, but apparently potatoes are excluded and I can't find a satisfactory answer as to why not. Processed fruits in juice drinks seem to count, so does a glass of wine?
What differentiates between fruit and vegetables that count and those that don't?
Have you had a read through the "What counts as your 5 A Day" link, at the top of the NHS page you linked to?
http://www.nhs.uk/Livewell/5ADAY/Pages/Whatcounts.aspx
It seems to answer most of the questions you've raised. Keep in mind that the point of these programs is to increase the variety of fresh fruit and veg - not to give you a list of foods you should eat, but to push towards better eating habits involving a wider variety of fresh foods (which, as the site says, are known to be healthier than processed foods).
According to that NHS page, potatoes don't seem to count because they're already consumed ubiquitously and often unhealthily. Wine wouldn't count because a) it's not fresh, and b) there are other health concerns involved.
