I had given WBJEE last year. Just for the sake of it, though. Didn't want to go to any college there.
Board level understanding and five months are enough for what you want. But yes, WBJEE tends to be tougher than most state entrance exams. It's almost on mains level, if not tougher. So make sure you are fully aware of the exam pattern. There is negative marking, and also multiple answer correct questions, so be careful. Practice all problems thoroughly, and previous years papers are a must. You must absolutely do previous papers, and time them too. Be careful about the negative marking though. Also, if you want CS/IT, you have to get a really good rank bro. As far as my experience is concerned, maths was tough and lengthy, physics was moderate, and chemistry was easy to moderate.
Hope it helps.
Best of luck!
P.S I'm also a dropper and a Bengali, but I'm not giving it this year. You have to go to Kolkata for the exam, keep that in mind too.