you can't real handle the logic behind early firearms in 5e's system. They were horribly inaccurate, but had ridiculous penetration while crossbows effectiveness were limited by shields and armour. So to make it work historically, you'd need to create separate  AC classes for non armour AC and armour AC. 


However on a successful hit....they were honestly about as effective. A war crossbow would probbaly push, maybe even exceed, a 1 ton draw weight. If one hit you and went through your armour, you were done. However 5e abstracts all of that. A wizards fireball, a barbarians great sword or dragons tail hitting you are all chunky salsa moments. No human, no matter what gear they have, takes one of those hits and gets up. HP shouldn't really be treated as a measure of health in most cases, but more like 'luck' or some other abstraction. 

When trying to create guns, your better off starting with crossbows as a base template. Then add some sort of mechanical features which abstracts the neat things about firearms in a fun way rather than a realistic way.  We do this anyways: Your fighter with a crossbow doesn't need to get out a windlass and spend the next 9 rounds reloading.