In 5e there is nothing called a Mystic Theurge, but that is because the way the rules are designed, it's redundant. There are many ways to design one.
In 5e see if you just multiclass say Cleric and Wizard that works better then 3.5 Mystic Theurge ever did. You will get a 9th level spell slot, up 5th level of spells known in both classes, and various features like the Clerics Channel Divinity, 4 out of 5 of your domain subclass features, destroy undead of up to 1 CR, Divine Intervention, and the Wizards Arcane Recovery, and 3 out of 4 Arcane Tradition subclass features.
Alternately you can just play a straight Wizard or Cleric but take the Ritual Caster feat which is basically a specialized form of multiclassing where you get a ritual caster book that you can put spells with the ritual tag into it from the class you linked the feat to. So a Cleric with the ritual caster feat Wizard could put spells like Find Familiar, Dectect Magic, Breath Water, Illusionary Steed, Tiny Hut, and more into their Ritual Caster book.
Way 3 is the Divine Soul Sorcerer. A Sorcerer who gets a feature at first level called Divine Magic that allows him to pick Divine Spells by picking spells off the cleric spell list as well as the Sorcerer's spell list, and a bonus cleric spell. He also can boost his own and his allies healing spells for 1 sorcery point, gets either angelic, demonic, or dragonfly wings depending on alignment affinity of his un/holy ancestor, and a major self heal at high level. And the usual Sorcerer stuff, metamagic, flexible casting, and extra cantrip. I like to take Ritual Casting Feat Wizard or Cleric or Druid or Bard in addition.
Way 4 is to play a Bard and cherry pick spells from the cleric and wizard spell lists using magical secrets.
Very interesting!
