Dual monitors waking from sleep very slow?
Assuming your cables are good and connected firmly, I would try resetting the NVRAM and SMC (in that order).

Resetting NVRAM

Your Mac use Non-Volatile Random-Access Memory (NVRAM) to store a whole range of settings. Here’s how to reset this:


Shut down your Mac. Yes, a full shut down, not just logging out.
Press the power button and then press the commandoptionPR keys. You have to make sure you press these keys before the gray screen appears or it won’t work.
Hold those keys down until your Mac reboots again and you here the startup chime for the second time.
Let go of the keys and let your Mac reboot normally.


Note: When you log back in you may need to readjust some of your system preferences (e.g. speaker volume, screen resolution, startup disk selection, time zone information, etc).

Resetting SMC on a Mac Pro

Follow these steps for resetting the SMC on your Mac Pro:


Fully Shut Down your Mac Pro
Unplug the AC power cord
Wait at least 15 seconds
Plug the AC power cord back in
Wait at least 5 seconds
Switch on your Mac Pro


Now use your Mac Pro as usual to determine if the problem still occurs. If so, try using your Mac in Safe Mode for a while to see if the problem occurs.

Booting into Safe Mode

Follow these steps to boot your Mac Pro into Safe Mode:


Fully shut down your Mac Pro
Restart your Mac Pro
Immediately press the Shift key and keep it down 
Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice).
Take a note of what happens (i.e. did your Mac Pro boot okay, are you still having issues with your screens waking up, etc)
Once you've tested long enough, exit Safe Mode by restart your Mac as normal


Let me know how you went and we'll go from there.