What is the last rank in the JEE advanced good enough to take admission? I think after 5000 you get useless branches. Is that correct?

Not at all,

Even if you end up with a relatively bad rank, you can opt for branches like Bio technology and somehow get into IIT. Work hard for 1 year and you can as well change your branch depending on your grades.

These branches also provide you with lot’s of course flexibility and you can as well do your minor in other streams of Engineering. You can use IIT tag to get into MBA or PHD later. Surely, there are lot of perks of being a part of top IIT.

Apart from IITs there are several institute which fill their seats on the basis of Jee Advanced ranks.

Hence, you can even get an admission into top institute with JEE rank under AIR 4000.

All The Very Best and Good Luck :)