would an i5 6400 and an rx 470 be enough for 1080p gaming and light video/audio editing?

Solution
Yes. Not ideal for all you want to do as rendering will take a longer compared to an i7 and you won't be able to run more than a couple of streams, but certainly capable if you only do these casually.
Hey there, Joe.

You should be fine with that setup. However you should make sure that you have enough memory as well (especially for the video editing and gaming). Other than that if you plan on streaming/recording while playing, it might not be a bad idea to get a faster storage solution as well, perhaps an SSD.

Cheers!
Boogieman_WD