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.
Best Answer
I enjoy (not all the time, but some of the time) games that try to very strongly simulate the real world and have asked the same question, as I do enjoy such a simulation. So you're not alone, don't let the 4e/indie crowd convince you "no one wants that." They don't and that's fine, but if you do, read on.
The pace of RL combat is mainly affected by the Clausewitzian principles of:
Friction is basically the mass of uncertainty that keeps most folks huddled under cover instead of running around like Quake deathmatchers. It's partially fear of death but a host of other factors that make the RPG paradigm of "doing something every 6 seconds without fail" patently unrealistic. Some games have an initiative system that somewhat simulates part of this effect; for example in Alternity you can lose one or both of your actions in a round if you roll poorly enough. You can also add bits of uncertainty to the rules to simulate friction - like one problem with many games is that movement rate, unlike every other part of a character, is fixed not variable, allowing confident exact maneuver. I often use a "Move check" and if you bork it you just may be exposed an extra round while trying to cross that alley under fire...
Fog of War is basically you not really knowing what is going on (this feeds into friction). In most RPGs you see all opponents all the time; making some kind of Perception check to detect them is by far the exception. But even some time outside playing paintball reveals to us that we are woefully unaware of our surroundings, where the enemy is, and where our allies are at any given time. Ironically one of the best ways of simulating this might be to incorporate computers into gaming, such that only opponents (and allies and terrain features) someone sees themselves would be revealed to them. You'd get a hugely different combat dynamic! Much of the firing in RL combat is basically blind and has less than even the usual minimum level of RPG granularity ("1 in 20") chance of hitting.
Both of these factors conspire to get you the slower move to decision that distinguishes real life combat from RPG combat, despite real combat often being "one hit and you're out of the fight." (Ablative hit point models are an attempt to approach this problem indirectly - by reducing one-shotting they try to get the longer battle times.)
Not many published RPGs deal with this topic successfully. Palladium Games' Recon!, a Vietnam war RPG, made a faithful effort towards it - an example is ambushes specifically, the ambushers vs the ambushees get very large bonuses/penalties to what they are doing to reflect the confluence of these factors. I've played it and this game does a good job of simulating the uncertainty of combat.
[Edit: I was in Half Price Books this weekend and was reading through Blood & Guts, a modern warfare supplement for d20 Modern, and it had distinct sub-rules for those wanting a more realistic combat experience.]
An ex-Marine buddy of mine wrote a couple really good articles (oddly enough, for "The Way, The Truth, & The Dice," the e-zine of the Christian Gamers Guild) about adding real world data-based realism to combat, using GURPS as the proximate rule system. The first article covers hit location/effects and the second covers friction (see page 22 of the PDF). They are worth mining for ideas.