Will I be able to play with players who don't have the 5th dlc?

Since there will be new skills and character models in the 5th DLC, if I buy it will I be able to play with other players who don’t own the DLC? And I don’t mean the Arms race, I mean the ordinary playthrough or takedowns.

Yes, you will be able to play with everyone. It’s the same rule as using DLC items.

Unless there’s gonna be a drastic change they haven’t communicated to us yet, you will. They will not be able to play Arms Race or use any new gear from that DLC but anything else should work perfectly fine.