In Windows, I used a program called autohotkey, which could map any mouse/key button to any other mouse/key. I had it set up to map the 4th and 5th buttons to Control and Alt respectively. That's all I need done. Could someone point me in the right direction? I found plenty on keymapping, but nothing relevant to the mouse

Thanks in advance

I can not vouch for this personally because I do not have a mouse like yours, but you might want to try package imwheel available through synaptic package manager (or apt-get)

Here is the description in synaptic:

program to support non-standard buttons on new mice
Many new mice include side or "thumb" buttons that have little or no function
in Linux, as well as a wheel that is still not used by all applications.

IMWheel supports these non-standard buttons and/or wheel operations by
allowing the user to map their input to key combinations which can vary
depending on the application in use.

Homepage: http://imwheel.sourceforge.net

Good Luck!