Hello all. I’m part of a gaming group at a university and I would love to DM a war campaign. Does 5E have rules for war gaming? I’m talking about battles between armies. If not what have you guys been using for rules? Thanks in advance. 

The dragonlance campaign has a board games for instances of mass combat. I’ve not played it, but I understand it’s designed for scenarios specific to that campaign. Not sure how easy it would be to adapt it to something else. 
There is a Matt Colville supplement or two. Many people swear by them, but I’ve seen others say they’re pretty lackluster. 
Beyond that if you are looking for all armies all the time, D&D is not the system for that. It’s for small scale fights and role play, not big battles. Most of the time, when there’s to be a big battle, it’s better to have the PCs act as an elite force with a strategic objective, not just in the thick of hundreds of swinging swords. 

for 5e, there are no official rule sets.

D&D isn't a mass combat game, and the rules don't scale well for it.  For wargaming, you have to look further afield than a system that sets individual capability as the basis and more for one that uses unit capability. 

1e (AD&D) had some decent rules for sieges and a few for scaled battles, but that's 40 years ago, lol, and 2e had a later expansion.