If one getsa rank below5000 in JEE Advanced?Can he get CSE Branch at an IIT?If, he is getting a new IIT,and is getting old NIT/BITS?

But according to the 2018 statistics,a student got CSE Seat in IIT Palakkad. What will you say about that?

IIT Pallakad - CSE at 4933 (Round 7)

Yes you are absolutely correct in this regard. But first of all the rank is very close to 5000 and secondly the cut-off might not work in your favor because of the increase in female quota seats and introduction of EWS category. These factors will most likely increase the cut-off for general male candidates that is why considering all these factors I said so! Last year cut-off are good for getting idea but they fluctuate with time as you will see in the upcoming rounds of JOSAA.