The flight will arrive like a US domestic flight (behind security). No one will be sent to immigration/customs. Bags will be checked through as long as they are tagged to your final destination when you first checked them.

However, I believe you will need to reclear security at T3, because there is no direct connection post-security from T5 to T3. Going from T3 to T5 there is a shuttle bus behind security, but as far as I can tell the shuttle bus does not transport passengers in the other direction because the assumption is that most people arriving in T5 are going through customs and thus need to reclear security anyway; Etihad passengers lose out because of this rule. Also, the train between T5 and T3 is closed for maintenance right now, so assuming you're traveling in the near future you'll need to take a landside bus from T5 to T3; many people make this connection so it should be signed clearly in the arrivals area of T5.