How to work abroad after working in a PSB for five years in India

You are already working in a Public Sector Bank so your primary strength is finance and accounts. Your experience will definitely help you in trying for a job abroad and there are some options which you can explore. The simplest that comes to the mind is that some PSBs have overseas branches and one can internally apply for them. The process of selection is tough as generally it is done through internal interviews but that is worth trying.
Another thing is go for some short course or diploma course in some niche subject which is in demand outside. For example 'Financial Services, Risk Management & Insurance' is one such area where there is demand of persons. If you have proficiency in computers and handling of financial applications then there are web based financial and accounting solutions being provided by the company to the customers and such companies hire banking professionals having good exposure to the online financial products.
Another area is investment banking and treasury operations. In many developed countries the return on money kept in banks is too small and common investors that is general public is getting low interest income. Some financial companies pool the money from the investors and invest it in other countries where ROI (return on investment) is better. These things are all monitored and done through the investment banking route. These companies also invest in Govt bonds and treasury instruments where also there are good opportunities in the fluctuating market. The yields on these investments change time to time and the investment experts take advantage of that for increasing ROI.
So, with these things in mind and increasing proficiencies in these areas one can apply in the outside companies by monitoring the positions advertised in job portals.

There are chances for people who are qualified and experienced to try for a job abroad work there. I hope you have taken the Passport from the Indian government.
There are many banks which are having foreign branches. If the bank in which you are working is having branches in foreign countries, you can try for a transfer there.
One of the best ways to get a finance job overseas is to work for a U.S.-based financial service company that does business internationally and have branches in India also. So while working in PSB you can try for a job in any bank or financial organisation that is having branches in India. Once you get a job there, you can join and try for a transfer to the US.
Another way is to go to the USA for doing a short term course and then try for a job after completing the course.
You can consider any one of the following courses abroad.
1. Certified Financial Planner Certificate Course
2. Certificate Course in Finance Accounting and Taxation
3. Business Analytics Certification Program
4. Chartered Financial Consultant course
5. Certificate course in financial risk management

As mentioned above you are having five years of bank experience and are searching job in abroad. So, at first, you should find out that there are any foreign branches of your bank in which you are working. If foreign branches are there then you can take transfer and settle there.
Another way is, there are many US-based financial companies where you can apply. After joining there, you can take a transfer. Besides, there are some short term courses and diploma courses which can be done for getting a job in abroad are as follows:-
1.Certificate Course in Finance Accounting and Taxation.
2. Business Analytics Certification Program
3. Certificate course in financial risk management.
4. Cost management accounting course

Since you have five years of banking experience and is interested to have an assignment in the foreign financial institutions/ banks while living in the abroad. While working as an employee of PSB, you should take all measures to be conversant with all the operations of the banks and should be conversant with the Banking and Insurance Law, Financial Risks, Measures to avoid bad loans etc. Once you feel comfortable with all sorts of such operations, look out the branches of your bank in the foreign preferably in USA because of prevalence of peaceful environment. If your bank does not have any branch in USA, you may try a job in other bank in India having its branches in USA as well.
You have to show your outstanding performance in your job and apprise of your interest of your transfer in USA. Based upon your work and consistent performance, they would provide you opportunity for going abroad.
The other way would be to acquire some short term diploma which could be helpful to you to have a job in USA with some job consultants. The following diploma courses could be helpful-
1) Certified Financial Planner Certificate course.
2) Business Analytics Certificate Programme.
3) Certificate of Risk Management and Insurance
4) Certificate of Financial Accounting and Taxation etc.