Monica,

At the rank of 5671 you can get lower branches in good IITS and good branches in newer IITS. Now if branch is your preference then go for new IITS. But if you want to have good college irrespective of branch you can fill top IITS first.

But I would recommend you to first fill top IITS it doesn't matter you get it or not based upon last year closing rank you should fill , fill it in a descending order..... Go as far as to the college in which you will take admission.

If you just want CSE branch then you may get it in NIT TRICHY OR WARANGAL OR SURATHKAL undoubtedly. So you can fill those first.

You have to fill every college and branches you wish for it doesn't matter you get it or not you have should fill it.

Then after filling choices you wish for in descending order , fill those choice which you are getting based upon previous year closing ranks then to be on safer side fill some colleges( but at last after filling the above 2 colleges) which you will get definitely so as in case everything doesn't go according to your plans you still have a seat.

Hope it helps