Even Binet could not define "intelligence."
I am not a good player, but have always maintained, "I can teach you how to PLAY chess, but not how to WIN chess" to almost anyone. So, IMHO, strategy and tactics are up to the individual. That said, the strategy and tactics lessons on this site are very helpful. Due to my limited ability, for them to help me has taken lots of iterations, and also lots of time. I believe they *have* helped improve my game, but only through due diligence on my part.
I re-suggest that to learn chess takes minutes; to master a lifetime (if ever, or even possible!).
Chess is like any skill, put in time and you'll get better. You woudln't expect yourself to paint or play the piano at an intermediate level after screwing around for less than a year would you? The potential for skill in chess is as immense as the greatest undertakings available to people.
5 months of training will still put you squarely in the beginner ranks, but 5 months of bullet I wouldn't call training at all. Your rating is where it should be. Play slow games (tournaments). Play often. Read books. Get a coach.
Well on that note I guess it would depend on your definition of intermediate. I would expect to be intermediate at chess in under a year but getting advanced to take far longer and master to take much much much longer.
But if you consider intermediate something like 1800 or 2000 then yes not in a year.