Wirelessly posted (iPhone 5: Mozilla/5.0 (iPhone; CPU iPhone OS 8_3 like Mac OS X) AppleWebKit/600.1.4 (KHTML, like Gecko) Version/8.0 Mobile/12F70 Safari/600.1.4)
I actually made the T5-T3 connection in less than 30 minutes on multiple occasions (from the time the door opens on the inbound flight to me walking onto the next flight). Things working in my favor: GE, TSA-pre and carry-on only. However, not a single time I had actually booked such a tight connection- every time I switched to an earlier flight.