I wonder what your level is now? If you go from entry to 1, five months is absolutely no problem, and there will be some difficulties in upgrading to the second level. If you want to improve to the third level by self-study, the possibility is too small. You know, the higher the level, the slower the promotion. For amateur chess players, the third stage is a hurdle from low stage to high stage. At this time, it requires a deeper understanding of Go theory and a more comprehensive basic skills.
Of course, it is not absolutely impossible. If you have a basic understanding of Weiqi and have a high talent for Weiqi, it is still possible to get expert advice.
Playing chess online is of little help to playing chess, because time is short, you can't think deeply, and you will develop the bad habit of playing chess casually. If you really want to improve, you'd better find a chess player who is two or three sons better than you, so that the chess game will be better.
By the way, as an old chess fan, I remind you that learning comes first. Don't let playing chess affect your study and rest.