Hey the answer you needed ,

Looks like you are looking for the engineering course in best colleges in Andhra Pradesh ,Since you are within 5000 rank in the AP EAMCET  exam there is a chance to get into the government colleges but still the time they have not published the cutoff of each institutions ,do frequently check the  website for the cutoff.

All the best!!!

Hope you are satisfied with the answer.

If you have any doubts ,feel free to ask.