Can you suggest government colleges that accept low JEE B.Arch rank( 5000-6000)?

Here is the list of the colleges you can get with JEE rank 5000-6000,  

1. NIT Pathna
2. NIT Raipur
3. NIT Calicut

These are the top 3 colleges, you can also go Rajkiya Engineering Colleges in Uttar Pradesh and Government College of Engineering, Bihar.

I hope it will help.