Your math doesn't work out. If you're new to racing, you started as a 5. You must complete 10 races to upgrade to Cat 4. You need 25 points to upgrade to Cat 3, wich could be done in 4 races if you won every race. You would then need 30 points, I think, to upgrade to Cat 2, which could be done in 5 races if you won every race (maybe less if you did stage races).
So, if you won every single race you entered, we're talking at least 19 races here.
Anyway, to answer your question, there are a few racers around here who went from 5>1 in a season, one of whom is now riding for a domestic pro team. He just raced with them a lot, and was consistently up there for the finish. I think he just asked them, or they asked him. Race a lot, with the teams you want to ride with, get results, and see if something pans out by September.