I stand corrected: sub-5:50 is possible.

Although most of the time improvement came from cleaner movement, there are two techs in this run that I hadn't shown in a "ACE" run before:

1. In the third room, it's possible to reach the top-left monitor early (opening the door to the final section), which saves around 0.3s
2. If you exit the teleport room with the items swapped (in my case, with the TP equipped to the Girl), you don't need to quickly swap the items while the Boy is in hitstun after reloading the next room.

But yeah, none of those would help save those ~9 seconds.