Is there an option to upgrade my iphone 5 to 5s?

Contact service provider but thru apple no.

there is a program Trade in in certain contries

Only options via Apple at this time involve a visit to an Apple Store. Is there one near you?

There are no Apple stores in India.

No Apple Stores No Apple policy

Only options will be carrier offering

Check with an Apple Shop like Reliance Digital at the Moments Mall in New Delhi. See if they have an option for you. There may something they can do for you.

Since there are only two authorized sources for iPhones in India, & Reliance Digital is not one of them, I doubt that will help the OP.

Since Apple Shops are directly authorized by Apple, there may be policies & procedures that you and I are unaware of. It hurts nothing for the OP to contact the local authorized Apple Shop for more details and ask about potential upgrades.

Since Reliance Digital cannot officially sell the iPhone 5S or 5C it would do him little good unless he is interested in upgrading to a gray market iPhone.

And Reliance Digital will probably be eventually allowed to sell the iPhone 5S. The overall question is whether or not they have an upgrade program at all.

The OP even acknowledged that this wouldn't be an option whatsoever until the 5S releases in India. What does it hurt for them to ask a simple question of his local Apple Shop?

Reliance Digital has not been authorized to sell any iPhones before, is there something with the 5S/5C that is supposed to change this?

They are listed as an Authorized Apple Shop on the Apple website.

https://locate.apple.com/in/en/storetype/?s=2&a=110005&f=lllll2l