i have been wondering how these two stack together, and want a clear answer to it. does it stack together or stack differently, as in if you have, for example, AR pro 5 with the 15% bonus and 1 complex light mod, does it add 15% first then the 10% separately? vice versa? or does it add them together for a combined 25%?

Base damage * 1.15 * 1.1.

Everything in EVE and DUST is based on multiplicative modifiers. Skill bonuses are the only thing added together based on level for the total modifier (3% + 3% + ...). Modules come with stacking penalties which you have to factor. There's a formula behind the penalty, but the simple way to remember is that the second module is only 87% effective and third is 57% effective.

So if you have 3 damage mods on top of Proficiency 5 the math is as follows:

x * 1.15 * 1.1 * (1 + (.87 * .1)) * (1 + (.57 * .1)) = 1.453x or a 45.3% total damage modifier

2 damage mods:

x * 1.15 * 1.1 * (1 + (.87 * .1)) = 1.375x or a 37.5% total damage modifier

Etc. etc.

I'm sure you can figure it out from there.