The checking content screen is a bit long-ish but not unbearably so. I haven't seen the rest of what you're referring to. I could check my PS4 copy in a bit but someone else will probably get to it before I do.
I was actually thinking of making a thread on the checking content load time.
I timed it and the game took 1min 34 secs to check for content. (your time might vary with amount of dlc)
The real problem is that the game doesnt need to check for content, the time it takes is literally the game taking time off your life.
Try this: Close out your doa5:lr so that it is not running (can also have it on the title screen), have a friend start a lobby and invite you. Accept the invite and the game wont check for content and it will just throw you into the lobby (all content accounted for).
This works on the xbox one, dont know about the ps4.
So it seems like some bad coding.