A good and solid answer was given already:
Modern firearms and grenades appear on page 268 of the Dungeon Master's Guide.
Please upvote that answer if you find it useful, I'm just copying it to comply with the guideline that every answer should stand on it's own even if the others get changed or removed.
However, a paragraph like this has been in all similar editions of D&D (2e, 3.5e and now 5e). I have tried that in the past but that little paragraph actually opens up a whole lot of other connected questions. For example how is armor treated if firearms are supposed to pierce them without problem. A lot of stuff that we take for granted in todays world simply has no rules. Not even conversions. D&D has no rules for chasing each other on horse drawn carts, so there is no easy conversion for modern cars either. The bottom line is, while this is an easy answer, it does not make for a good game conversion, it only leaves you with hundreds of similar questions that don't have answers in the DMG or any other official D&D book. You will probably not be satisfied with your game experience if you take this answer and start playing.
So let me challenge the frame of your question. You want to play a walking dead style campaign with modern weapons. What you have as a tool to do so right now is D&D. And you run into problems because D&D was never meant to do that. There is no modern setting in D&D, it aims very specifically at sword & sorcery, dragons and heroes. No guns, no electricity, no medicine, no internet, but instead you got guys casting spells left and right.
Your question is a bit like having a car, and wanting to have a good sailing trip on the lake with your buddy. That's great. But you run into problems because your car isn't suited for it and now you are asking how to raise a sail on your car because you haven't found the mast yet. Well, there is no mast. It's not meant to do that.
While I'm sure a lot of people will be eager to sell you a mast and a sail and something to waterproof your whole car, let's look outside of the question for a second. How about getting a boat?
Looking around this site for a system that supports a modern day zombie apocalypse, there are threads here, however, they tend to be opinionated and not a good fit for our format.
What would probably work best is to find your local store and just ask them. If it's a good store, they will present you some systems that fit your needs and leave you at a quiet table where you can browse all of them to decide.
To sum it up: get a system that suits your needs. There are plenty out there. Go grab one and have fun.