can I get cse at amrithapuri in open quota with rank 5744 in which round

Hello student.

5744 is a good rank for you to fetch you a seat in amrithapuri(kerala) campus in open quota. But the branch of computer science is a demanding one. NOt just that branch, branches like computer  science, electronics and communication engineering, electrical and electronics engineering etc are sort of demanding branches.

There might be chances to get computer science. Might be in 2nd round or 3rd round of counselling. Apply for the university, attend the counselling. People might not be attending because, they migght be preferring nit's etc.

So you have chances.