In addition to the playbook showing the wrong increase, they also describe the initial British support incorrectly as 1. At the start of support phase 6.4 the British actually have passive support in New York City (2x1) and passive support in Quebec City (1x1) for a total initial support of 3.
The result, 3 initial support plus an increase of 5 support will result in a new total of 8 support. From what I've seen so far, (British) Total Support can always be "double checked" by looking at all of the cities and colonies on the map with British support and adding them up.
New York City does not add support because of the French blockade. The initial count of 1 is correct.
That being said, I also see the support going up by 5 instead of just 3.