Lots of links talk about the ports required for the AD connection and in my environment below ports are enabled and able to add the client to the AD with DNS registred.

TCP_636
  TCP_3268
  TCP_3269
TCP_88
  UDP_88
  TCP_53
UDP_53
  TCP_445
 UDP_445
  TCP_25
TCP_135
TCP_5722
  UDP_123
  TCP_464
  UDP_464
  UDP_138
  TCP_9389
  UDP_137
 TCP_139
UDP_49152-65535
  TCP_49152-65535

Refer:

https://isc.sans.edu/diary/Cyber+Security+Awareness+Month+-+Day+27+-+Active+Directory+Ports/7468