What happens if you transcode the mp4 to a different codec.... let's say a QT PNG, ProRes or Animation?
And I gotta tell you... 5 minutes and 30 seconds of ANYTHING in AE is a huge amount of time. I bet you could save yourself a lot of aggravation with a different workflow, beginning in Premiere Pro first.
Premiere does the exact same thing. I'll give a different codec a try.
I converted to QT format and tried loading. The sound stops at 1:00 exact into the clips, regardless of whether I load into Premiere or AE. I thought it might be a scratch disk issue but I have ruled that out. I honestly have no idea what is going on but it's extremely frustrating.
If both Premiere and AE are having issues, this points to a more fundamental codec issue on the system.
Do you have any third-party codec packs installed? I've seen the K-Lite pack cause weird issues in the past, but a few of the other ones have made issues too.