You want a program that converts higher frame rates to 24/5fps. I've never used AE but considering how extremely advanced it is, there should be a tutorial on how to do it in AE.
Apple's Compressor is my favourite choice, it's basically a program that imports footage from your SD card to your computer using some crazy smooth settings, I even use it for importing 24fps 1080p from my SD to my laptop just because it looks better after compressor handles it.
You're basically looking for an importing program that lets you choose the export settings (similar to when you're exporting from AE), google a little bit for a couple of minutes and you'll find something. I think there's even a plugin for AE that does this.
I did a little bit of researching and I found out people use Quicktime Pro to do this process, hope this helps