Hello,

Yes you can give GATE exam simultaneously work, no need to leave job. If you clear the cutoff marks for PSUs you will get a call from them for interview.
The cutoff marks are really high such as 70+ or 80+ in GATE exam. Working in any PSU is a reputed job and gives you good lifestyle with added perks. There is also job security.
Also you have worked in a company for 5 years you have good experience. This is an advantage during interviews.
The gate scores are valid for 3 years for M.Tech admissions. This is not the case for PSUs. You will have to give GATE exam in the coming year and clear the required cutoff.
But you need to check certain  PSUs which have age limit criteria.
You can refer careers360's article about PSU recruitment through GATE. This will help you clarify your doubts.
https://engineering.careers360.com/articles/psu-recruitment-through-gate
I hope I have answered all your queries properly.
All the best!

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