Legal Implications of Non-Payment of Salary
Legally speaking, by not paying your salary on time, your employers have violated the terms of employment. Therefore, you are free to leave with immediate effect. Once the terms have been violated, under the Indian Contract Act, the contract comes to an end, and none of the terms hold true.
So, the only rights left under the contract of employment are that you have a right to take legal action against them for non-payment of salaries. In any case, is it likely that they are going to pay you the balance salary? Do you think they will be cooperative when you leave? Looking at the past history or even the current situation, it does not seem likely. So why bother adhering to their instructions on the notice period? Just walk off to your new job and write off this as a bad experience.
Any company you join in the future, just clearly tell the HR team that you left the previous company because they did not pay you five months' salary and therefore you do not have the necessary leaving documents.