Considering your rank in jee mains which is 5666 , obc category. And taking into consideration previous year rank cutoff , you can get into approx all NIT's with good branches but you might have to wait for some round. But you won't get good branches in top NIT's. 

ou can visit JOSAA website and see previous year rank cutoffs for different colleges and then prepare a list of colleges you are going in. It will be easier to fill the preferences then in josaa councelling.

All the best.

thank you.