Reporting back - we were able to do this successfully and it’s quite easy because we arrived in T3 and were departing from T5.

Recapping:

• Arrive in T3 (cabin bags only)
• Follow signs for T3 connecting flights. No need to go through passport control. But you will need to go through transit security check in T3.
• Tell the person at the boarding pass check just before security that you want to visit the Amex Centurion lounge.
• Go through transit security.
• Walk down the long passageway. As soon as you enter the main T3 shopping/dining departure area, you’ll see the Centurion lounge entrance on your right.
• After you’re done, retrace your steps. When you reach the T3 post-transit-security area, chat with the folks at the desk and indicate you want to get to T5. They will let you through a special double-door.
• Take the airside transit bus to T5.
• At T5 you have to go through security again, so remember to leave a sufficient amount of time for this.
  

Thank you to everyone who documented the steps!