Im not asking for the basics. I'm looking for any fun tips or advise you might have for making combat run smoothly and for raising the tension. I don't want my game to feel like a math equation and I feel like combat is where the equation comes out most. What can I do to make combat feel more engaging? 

Describe the combat in detail. How the monster missed, what happened when the character hit, how it looks when injured etc. Also, to speed things up and keep players more engaged, have everyone roll damage dice along with attack die simultaneously. Those two things have really made my table more fun. Length of time from when a player attacks to the next time is crucial. A good turn for a player should be under 30 seconds. The faster the rounds go, the faster they have to think about what they want to do and the more tension and excitement there will be.

Thanks, this is some good stuff

Some ideas:

Throw in lots of environment interactions. Chandeliers for swinging on, pits of lava/acid to push things into, simple pits to push enemies into to delay them, columns to knock over onto enemies. Then reward the players appropriately for using these things, make their crazy plans *work*. That way people will be always on the lookout for clever things to do besides "I attack (roll attack + damage)".

Make the enemies behave thematically rather than like video game enemies. See, e.g., http://themonstersknow.com/ . Undead shamble in hordes, whereas predators try to pick off a weak character and run off with them, whereas a well-trained troop of enemies know how to do focus-fire, etc. This will change around player tactics - against a shambling horde the tank just needs to stand in front and take all the hits, against a different enemy the wizards better use cover well otherwise they get pincushioned by archers, etc.

Thanks. This is all super useful

Some good suggestions so far; I'm a big fan of keeping monsters thematic in their combat, and involving a dynamic changeable environment in the combat.

While it's tricky to do with 5e combats, which tend to be short - 3-5 rounds? - I like to have the tactics of the antagonists change, according to the conditions of the combat.

What they are trying to do should change with the Player tactics, and how they are seeing the battle progressing. Sketch out some thematically appropriate tactics, and figure out under what conditions those tactics will change.

This includes everything up to, and including, running away, or digging in and fighting "to the last man", although digging in and fighting, an orderly fighting withdrawal, and a headlong fleeing route, would have different trigger conditions, and possibly involve some saving throws.

Remember, Combats don't exist in a vacuum, or exist just for the sake of Combat. Everyone involved has a goal, and a motivation. How they are acting in that Combat will be influenced by how the tide of the battle interacts with that Goal: Orcs defending their homes and families will behave differently in combat than an Orc hunting party who just happened to stumble across the Party.

This is good stuff

That prompts an interesting question. You say you don't want the Combat to feel like a math equation. Are you happy with the level of math in RAW, but don't want to add more through additional complex mechanics, and you're just looking for pointers on how to make RAW combat more interesting and flow more smoothly; or are you looking to rip out the math and use a more fluid and intuitive narrative form of Combat?

The answer changes what you want a lot.

A narrative based alternative combat system could have a better flow, be easier for Players to pick up, and be a lot more streamlined. However, it's probably less consistent  (being more influenced by factors like "the rule of cool"), have less verisimilitude, and be less tactically complex ( which some tables will like, and others not ). 

As for RAW combat, I gave you some of my ideas for more interesting and tactically dynamic,  but if you're looking to manage flow, I'd point you to The Angry GM article: How to Manage Combat Like a Motherf$&%ing Dolphin.

If you're keeping RAW tactical combat,  and you're using a battle mat with miniatures (or markers of some kind), and you're finding that slows things down - I find a good middle ground to be abstract maps, which can still keep the combat tactically clear & organized - without have to count squares, measure distances, or move figures around. I do this, and I basically sketch a not-to-scale abstract diagram of the combat theatre on a big piece of paper.

Narration is big. Let your players know how big the hits they're doing are and how big the hits they're getting are as well. Does a dying NPC need to flee or give up? Give them a look of worry on their face as they look around thinking of their next action. Combat can be just as effective at storytelling as roleplaying.

I'll put in a voice for an opposite take from that a few posts above - I think using minis and maps well *helps* stimulate interesting combat rather than suppressing it.

When doing theater of the mind combat, I always had difficulty imagining exciting this to do. I couldn't easily tell where terrain was or where enemies were with respect to the environment, and so it was easiest to just reverto "I attack" or "I cast a spell to hit as many enemies as possible'. In the campaign I'm DMing now, with a map and minis, on the other hand, the map can have all sorts of details for players to latch on to. Twists and turns in the corridors, pits and barriers and furniture and stairs and so many other things. If you have a rich map, players will naturally want to use the stuff they see on it, and if you reward that they'll keep doing it.

I don't always have a grid on the map and when I do, I don't require that players move along the grid - it's just there for a reference for distance/size.

I agree that maps and minis are a great visualization tool. I think they add overhead to the combat, and slow it down as well.

It's just a question of which one you want to emphasize: speed or ease of visualization. I've done both, I've liked both - but for different groups.

I think you can have theatre of the mind, coupled with abstract maps, and rough GM sketches that can convey that level of detail - but it takes some skill on the GMs part. Maps and minis are a lot less dependant on GM description - although I do have a healthy dose of respect for GMs who can paint minis well, and build engaging battlemaps, so I won't say that takes less skill :)