A $5000 USD EFC will barely cover the round trip ticket from India and all of your living expenses for the year. So you’ll need to limit your search to colleges that will provide full tuition, room, board, books, etc. You’ll probably also need to get a work-study job.
That doesn’t leave a whole lot of options for you unfortunately. There are lots of students from India who do their undergrad in the US. But most of them are extremely wealthy. The admission offices know this. The top colleges could fill their class 10 x over with plenty of students just like you, most of whom would be full pay. This has nothing to do with your accomplishments and self-worth. Colleges are just running a business. So don’t take it personally.
If I were you, I would shift my attention towards an affordable option in India. Have you taken JEE? Why are IITs not an option for you? Have you thought about NUS (National University of Singapore)? I believe they have some scholarships for internationals.