Mouse 4 and 5 are real buttons (aka forward and back). Games can recognize them without mapping them outside of the game. Games like Metal Gear Ground Zeroes don't because of ignorance while it was being ported, but for most games I've played, especially first and third person shooters, should work just fine.

I'm not sure which mouse you have, but in it's drivers you can probably map two of them to those defaults. They should be Mouse 4 and 5, or possibly listed as something like "Browser Back" and "Browser Forward". The rest beyond that would be best mapped to keys you don't use in games, but ones that you are aware of so that you can map them in the rebinding menus in games. You can also consider using some of them to duplicate keyboard buttons you already use with your left hand, but ones that might prevent you from moving in a certain direction with WASD. Such as 1-5, Tab, Alt, Ctrl, VGTR, etc. I'd say just sit down and really think about it, and work it out one day, hopefully something you can use universally, where all you're mapping would happen in the games. Once you start having two or three mappings in the mouse itself, and you get confusion about which goes with which game, etc, so try to stick to one mapping on the hardware and more specific arrangements within the games.

Just as a basic example to get you thinking. Some people have Q in CS:GO mapped to last weapon switch. I want last weapon switch on my closest thumb button for easy scope canceling with the AWP. I could map one of the buttons to Q and use that, or I can have the mapping on the mouse elsewhere on the board, moving last weapon to that key, thus freeing up the extremely easy to hit Q key for something else.