Hi Harrison,
I'll take a stab at this one. Just a disclaimer though, while I own a midrange sound system and do run sound once in a while, I'm more of a light guy and can't compare my knowledge/experience to a lot of the more seasoned audio professionals here. That said, here's how I'd set up your system:
Hook up your GX5s to your Peaveys, one to the 115s, one to the 215s. As far as their physical placement goes, be aware there will be some interference between those speakers if clustered together. Again, I'm not an expert on that sort of thing but a quick search through this forum will turn up plenty of reading about it. Search comb filtering for starters.
Knowing nothing about the amp or subwoofer, I'd take a random guess that they are meant to be hooked up together seeing that other amps and speakers are pretty good matches.
Yes, you will need to buy a crossover. I personally use a BBE DS24, but there are many options available. I chose what I did because I am a mobile operator with a few different speaker combinations, and this crossover can save different profiles as well as handle a few more advanced features such as delay. A search or post in this forum (particularly the lab lounge) will probably yield some more input to this as well. Once you get your crossover, just run your mains out from the mixer into the crossover and then out into the appropriate amps. Let your ears help you set the appropriate crossover frequencies and filters.
Hope this helps!
-Jeff