Anyone can conquer the world. In 5e I think a Lore Bard would have the easiest time between high charisma, and expertise, and peerless skill, and glibness they should be able to roll somewhere from high to outrageously high on any social check, and parlay this to raise armies and funds with relative ease and bolster them with a broad set of high level spellcasting as needed, including a limited access to all spell lists.
To me the question is not could a 5e Wizard conquer the world but what a 5e Wizard's world conquest looks like, and how useful their wizardry is in world conquest. I would say generally what they have going for them is the highest potential versatility of spells. Any wizard conquest that does not play to that could probably be better achieved by another class. Furthermore any tactic that just requires occasional use of more obscure pulls from the wizard list could be achieved by anyone else who has access to Wish and sufficient time.
So what does the wizardy path towards world conquest look like? That's going to depend on the world and the wizard, but some key elements should probably include:
1. Mind control: Don't rely on this too far, or you will build a very weak empire, but from time to time there is going to be the need to convert strategic people to your way of thinking. A Wizard should know the spells for this. For world conquest there is particular value in spells like Geas and Mass Suggestion that have the potential to be upcast for very long durations. For this reason I think one of the best overall world conquest wizards is the Enchanter, as they both can more easily mind control people without the people remembering, and get free twinned spells on their single target enchantments, which stretches the value of their high level spell slots.
2. Gaslighting: Related to mind control, but moving beyond crudely commanding people directly, there is also the potential to just subvert their concepts of reality through illusions, Modify Memory, manipulating their dreams with Dream, all sorts of things. Similar tactics to direct mind control, but this is why we are using a Wizard, because they can know a bunch of similar spells and use precisely the best one for every occasion, rather than trying to solve every problem with the same 15 spells like some crude Sorcerer.
3. Oz the Great and Powerful: While we are on the subject of illusions, there are doubtlessly those which the Wizard can use to make the common folk think they are a much more powerful wizard than they are, if not some manner of god. Between illusion and transmography it is important to show yourself taking all manner of imposing forms, and never let out the secret of your actual fairly mundane nature.
4. Stay Removed: While we're being mysterious it is probably worth noting how great the Wizard spell list is for not actually going places and doing things yourself. You can create a homunculous to be your eyes and ears, you can send simulacra to go do anything too dangerous for yourself. You can use things like Sending and Dream to communicate at great distances. There are also all manner of things you can conjure for an hour to go do your bidding. There are also a variety of ways to ward your home or wherever you are or to keep yourself and all your valuables in pocket dimensions.
5. The Panopticon: People who think they are likely to be under surveillance will stay in line whether they are actually actively being surveilled or not. Make it clear to your subjects that at any time they may be being scryed upon and judged by the almighty Wizard-Emperor, and many will obey. Walk your lands invisibly, or in many guises, such that they never know when a stranger or a friend or a shadow might be his imperial majesty or one of his agents watching and waiting for insurrection.
6. Contingency planning. Obviously you have a clone ready at all times. Obviously you have a choice protective spell Contingency-ed at all times. You should also be ready to go ethereal and/or just bamf out of any place you are at any moment. Basic wizard common sense.
7. Insta-Construction: Between Wall of Stone, Galder's Tower, and Mighty Fortress you have a lot of ability to quickly erect temporary fortifications, and potentially to make them permanent. Now you don't want to spend all your time and spells building castles, but when a 20th level Wizard's army is on the march or besieging an enemy fortress their is no reason they should not be well fortified.
8. Transportation Infrastructure: You can make perminent teleportation circles. Make perminant teleportation circles. You and your entourage will have to cover a lot of ground if you are to keep a whole world under your thumb.
9. Occasional Displays of Overwhelming Power: Look, if you don't occasionally Meteor Swarm an opposing army or turn yourself into a Dragon, then you're just missing out on the fun. Generally the sort of combat which is the bread and butter of D&D gameplay will not build an empire, but used ostentatiously at the right moment, it is what will tell your would-be subjects who the level 20 Spellcaster is, and how insignificant they are by comparison.
10. An evil army of undead. We'll put this on the maybe pile. Certainly it's one way to go, but generally it is going to tip your hand that you are a damned villain, and a 5e player controlled force of undead is never going to be of world conquering size, and the larger it gets the more of a burden it becomes on your spellcasting to maintain it. That said you can get perma-minions through Finger of Death, and having a few eternal sentinels who don't require any food or sleep will be good for guarding the distant outposts of your empire. Just be sure to get the PR department working on it. Otherwise avoid necromancy, but do know the spells for it because you are a wizard and that is how you roll. If your non-undead army is vanquished and you are cut off from all reinforcements, then tomorrow you recycle your dead.
Pick and choose tactics as you like, and use them to build upon, strengthen, and support more conventional empire building, not in place of it. The important thing is to use a substantial variety of tactics because that is the reason to do this as a Wizard rather than a Bard, or if you are using really narrow tactics a Sorcerer or Warlock, all of whom have a tremendous leg up on you in gaining wealth, followers, and conventional power due to being charismatic and any of whom could be built to do particular magically enhanced tactics better than you. The Wizard's strength is in being able to dabble in every form of magic useful for world conquest and switch between them freely.
