The difficult part of stage 5 is the timing of this moving platform:
When I took the right ladder earlier in the level (which is faster in theory)...
Memory address 05B7
At the left turnaround point, the platform reaches X-position 088.
It moves 2.5 pixels per 3 frames.
So its X-position goes like 088-091-093-096-098... when it moves rightward.
The right turnaround point of its journey is 010 after going beyond 255.
So the rightward pattern finishes as ...253-000-002-005-007-010.
Moving leftward is just the reverse order. 010-007-005... until 088.
So 178 pixels from one side to the other at 2.5 pixels per 3 frames.
The whole one-way journey takes 213 frames.
So if the platform is traveling away from you when you reach the cliff, you'll have to wait almost double that amount (426 frames = 7.1 seconds).
So you have to manipulate the position of the platform with sub-optimal play earlier in the level.
It first appears at the memory address when you reach this point:
When I tried the left ladder instead, the platform didn't show up at 05B7. I don't know its memory address. But on either path, going through optimally is going to lead to a wait of about 6 seconds for the platform. It has to be manipulated by wasting some frames, like the big man on stage 2. It's trial and error.