They are both correct, you rarely get time off after basic. Besides, by then you don't even have 5 days saved up. You only get 2.5 days per month. My advice would be to take 4-5 days off after AIT and then try to save up your leave time.
Personally I save up all my leave time and try to take 30 days all at once, depends on your command though. It's much more relaxing that way. I always have at least 60 days available. 30 for vacation and 30 in case of an emergency.
Good luck at BMT. Don't stress too much, just follow the guy in front of you and you'll be fine.