This run has no mistakes. I can really only say that Jump Training, There and Back Again, and Platform Party looks sloppy to me. However, no level blows me away except Bumper Training, so I have some more time to save here.
I successfully implemented the Bumper Training "bumper hit" and Pitfalls edge hit in achieving this 5:04. I was getting sub-5's on Jump Training by adding the tweak where I jump on the railing, but the potential of this tweak didn't realize itself in this run.
Next on my implementation list to save ~2 second:
Grand Finale like how WRR#2 does it Xelna's nifty jump pattern on There and Back Again Maybe the edge hit on Learning to Roll? Depends if I can find or borrow a consistent enough setup.
2nd place is a good goal, but it is clear to me now that my limit is past the 5 minute barrier, so I think I'll grind for a 4:5x eventually :D