Good quality comes with long render times, and there is nothing you can do about it in any program you use. I would suggest you to convert the avi file to a different format to compres it, like MPEG-4 to get the best quality with the lowest bitrate. Just google for "avi to MPEG-4 converter" and you should get loads of options. Experiment what quality you can get under those 5mb. Also I would suggest you to do some reading about this topic to better understand how all of it works to get the best results.
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