Shadow would be a competitor too, if she can pull off 2 SSs in 5 secs, which I'm not really sure she can...
It might be possible with the perfect confluence of events, but with 175% on my weapons screen, and the weight/power bonus for passives in Rank 4, I believe my Shadow Strike's refresh is a little over 2.7 seconds. Once you've factored in the animation and travel time, I figure it's probably closer to about 7 seconds for 2 Shadow Strikes under very ideal circumstances.
I'm more inclined to agree that it's probably a grenade class with power bonuses. My personal guess is that it's a cluster grenade class doing a combo. Because of Flamer DoT, it might even be the Vorcha Sentinel, especially because of the ability to cause more than one detonation per throw, and the ability to spam grenades very quickly.
I figure it might be 1 second Flamer, followed by 2 or 3 throws of cluster (I doubt 3 is possible in under 5 seconds.)
It also assumes a good spawn spread, since I'm considering multi-target damage, as opposed to just single target. But, assuming that an Atlas was standing in the middle of a bunch of mooks, you could conceivably hit the Atlas was a heck of a lot of damage in 5 seconds, from Flamer, clusters, and two (or maybe even 3) Rank 12 combos.
Obviously if you remove the surrounding mooks, the total damage to the Atlas actually goes down, as you'll only get a maximum of one detonation. Vorcha Sentinel is probably a strong candidate under very ideal circumstances.