IMO, I think the "resting a full five minutes after the last warmup (210x2)" is a mistake.
You might be cooling off. That's really not enough load to cause THAT much fatigue.
I just switch weights and wait like 30 sec or so and then do the first workset.
3x5 should be somewhere around 80% working load.
210# is your case is only 65% or so....for two reps.
There's not THAT much fatigue from a double at 65%.