Thanks for the ask to answer.

Firstly I would like to say that 5 months is quite sufficient time to prepare for JEE mains. I prepared for mains and advanced myself in just 4 .5 months with just a correspondence course. Also I agree with Shiv Gupta: saying just JEE Mains is just immature. Advanced has basically the same course. It is just a little more 'advanced'.
Well the way I went about it was that I prepared a comprehensive time table. By comprehensive I mean i charted out which topic I would cover on which day and how many hours I would devote to it for each day for the next 4 and a half months, making sure that I would cover the entire syllabus and difficult topics at least twice. ( I hadn't studied much but payed a little attention in class and knew/ guessed which topics would give me most problem.) Now this is not very easy and such a long scale prediction is difficult, so give more than extra buffers, but it is Essential. It took me three days to do this but it payed off.

Now once you're clear on how to do things when, lets start with what to do. You need to study not to solve problems but to grasp the basics and understand them so you an apply it to any problem. Practicing problems is very essential but only after you have completely understood the theoratical aspects. Your concepts should be so clear that you can derive any formula you forget.
Take tests regularly. For this I used the tests of a two year correspondence course which had tests for all the chapters I had covered. This builds confidence and the knack to solve questions in limited time.
Finally I would like to add that when you are near the exams make sure you have taken enough mock tests. Here are a few bibles :
Physics : H C Verma (I E Irodov if you're feeling adventurous)
Chemistry: NCERT ( You can refer Morrison and Boyd for organic and R C Mukherjee for numericals0
Maths: Amit M Aggarwal for calculus(after NCERT), S L loney for coordinate geometry.
Hope this helped