My comments were well received enough I thought I'd contribute an answer. I run theater of the mind combat preferentially. I couldn't always get away with it in 3.5/Pathfinder, but in Basic and 2e days I did this exclusively. We are even doing this more in Pathfinder nowadays as we get more and more bored with the tactical tabletop combat. D&D Next/5e is fairly similar to 2e in metaphor so I believe most of these techniques will port well.
Theater of the mind provides quicker and, frankly, more interesting combat scenes - but the primary risk that comes with it is players feeling hosed, that too much of the power is in the GM's hands, and that they keep getting told "No" arbitrarily when they want to reach someone in combat or whatever. This is why D&D had been moving more and more to minis and defined rules in the name of "player empowerment." Here's how to do theater of the mind without reducing player agency.
Put information in your players' hands.
Be clear with your descriptions. For this to work, you have to be clear and the players have to pay attention, or else you get a lot of "well I wouldn't have charged if I had heard there was a chasm between us and then..." Describe the most important elements (obstacles, opponents, how those opponents are armed) and don't be afraid to reiterate it each round.
Even if not using a tactical map, putting a quickie room sketch on a whiteboard or whatever can help a lot - in our Pathfinder games nowadays, "mapping" is just the GM continuing to draw the map on the whiteboard, and rather than use a tactical map we just refer to that and say "I run over near that altar thing..." If pressed we add some X's and O's, football play board style, to show relative force dispositions.
You'll want to be fair and have a clear "take-back" policy for the table in case of mishearing - but it's OK to not be too generous there, as it will encourage people to pay attention. In general, give them the benefit of the doubt.
Put decisions in your players' hands.
Firstly, let them have some discretionary input into the narration. I learned my lesson on this playing Feng Shui, where I learned if the PCs are fighting in a pizza parlor and someone wants to pick up a pizza cutter and slash someone, getting out of the way of that as the GM and letting them declare there's a pizza cutter nearby and use it has a lot of upsides to that. After playing Feng Shui I was so much better as a D&D DM. Let them riff off the environment, only vetoing clear abuse.
You also want to encourage players to explain both what they want to do and "why" - their intent and stakes. "I want to get into flank around the orc with Jethro, and I'm willing to risk an AoO to get there," for example. Similarly, you as the GM want to state options and stakes as well - "You can do that, but there's a chance that you'll fall in that pit." Some quick negotiation and being very specific help here. "I want to swing on the chandelier, and I'm willing to risk a fall," says the player, envisioning a max of 2d6 damage based on the room description they heard, but the GM is thinking 10d6... If you wait till after the slip and fall to have that discussion the player gets irate; if you set the stakes up front everyone's on the same page.
Put outcomes in your players' hands.
Put the outcome in the PC's hands, ideally via a die roll from some attribute of their character. So if they want to know how many creatures they can catch in their Burning Hands spell, you could respond "Two, but you can roll Spellcraft (or Int, or whatever) to try to get three, with the downside that if you fumble you'll burn one of your buddies in melee with them." I use this in naval combat in our current Pathfinder game - when a PC Fireballs the other ship, how the heck do I know where every one of the 30 enemy crewmen are? I say "Roll Spellcraft," and based on the result is how many pirates got fried (generalizing assists and success as a kinda standard "+2 per 5 over" rate helps a lot here).
Same thing with movement. I have all my players convert their movement into an actual "Move bonus", +2 per 5' of movement, so a 30' move is a +12, for example. (Side rant, the conception of movement as fixed when everything else in the system is a variable is one of the greatest missed opportunities in D&D design and all the other games that blindly inherit their metaphor from it.) "I want to get around that orc and flank him with Billy!" "OK, roll Move. You're not even inside the door yet and there's a bunch of other orcs, so I'll call that DC 20, fail means you get to melee but not in flank, fail by 5 means someone AoOs you on the way."
I also used a house rule Luck stat in 2e - see my answer on How to add and use a luck stat? for more - to help determine other elements like "Who's standing on the trapdoor?" Because if a player is rolling for it and/or making risk/reward decisions, then they feel that the outcome is in their hands and not yours.
One last thought - make character options that a PC has paid for worth it. Some options are hard to quantify if not on a battlemat (like the Lunge feat from Pathfinder). As the GM, you basically want to keep stuff like that in mind and give them a benefit for it from time to time. If, for example, you're telling people they can't reach opponents a good bit in battle, and someone has the Lunge feat, turn it into "you reached them!" automatically once every combat when they plead "but... Lunge!" Basically whatever the option is allegedly for, let it do that.