There's no right or wrong answer to the question.
If you're looking for mechanical optimization, then there are some things that you can do with multi-classing that produce interesting outcomes. I haven't yet experienced combos that are broken to the same extent as what I've seen in 3e D&D.
However, after 100+ sessions of 5e D&D (almost all as DM for a group of 4-6 players), I'll make the following observations:
1) As stated by Wik, there's a lot you can do with the whole background/class/race thing. I'll go a step further, and also add feats to the list. One of my players decided to "get religion" by taking the Magic Initiate feat. He was playing a wizard, and wanted to be ordained into the faith of the God of Magic. Rather than taking a level of cleric, he took the Magic Initiate feat and selected cleric spells as his options. I thought this was a brilliant decision by the player; he'd roleplayed his faithfulness and devotion since the character began, and the spells he chose were not "optimal" choices or intended for some kind of combo. It was pure story-telling.
2) Personal Opinion Time: I have a known aversion to multi-classing because of one player in my group. He only plays multi-class characters (or single-class monks, oddly). And it's torturous. He'll create a 1st level Fighter. Then, at 2nd level, he'll go cleric (for three levels). Then, at 5th level, he'll go ranger. And here's the kicker: when I ask him why he's become a cleric, or a ranger, his response is always: "...because I need it for the build. If I combine this with that, then I get a huge AC... or I can use my Bonus Action to do the following... etc". I kind of hate this. The famous literary character Conan may have started out as a Barbarian, then Rogue, then Barbarian again, then finished as a Fighter... but at least that's a progression based on the character's story and life experiences. Planning out your character's multi-classing based on some Internet-posted combo-build just annoys me.
3) Finally, I've seen a few other players attempt "honest" multi-class builds that try to do many different things well. I've seen one player who didn't want to be reliant on other players to heal him, so his fighter took a few levels in cleric - simply so that he could self-heal. I've seen another player who took a level in wizard simply so that he counted as a spellcaster and could use certain wands/staves/scrolls. These weren't power-gaming choices, but they weren't (in my opinion) much better than the combo-building guy above. They ignored the fact that D&D is a team game, and your character probably can't be all things to all people. Some of these multi-class characters ended up creating arguments at the table ("I don't need your cleric! I can heal myself!", "No, I don't agree that the 8th level wizard should get the spell scroll! My Fighter 7 / Wizard 1 is also a wizard!", "Why the heck did you waste a level on wizard? You're our only warrior! Why are you trying to do my job?").
Now, those are just some of my experiences. And, to forestall the inevitable helpful suggestion, I continue to allow multi-classing in nearly every case because I try to be a "Yes DM" rather than a "No DM". And, fortunately, the majority of my players are perfectly happy with single-class characters.
However, if I've learned anything, I'd return the question to the Original Poster: "What are you trying to achieve with multi-classing?". If it's something story-related and non-optimized, such as modelling a genuine change in your character's career or outlook on life, then good for you. On the other hand, if you're looking for power-gaming tips or what produces the most Damage-Per-Round, then I'm the wrong DM to ask... or play with.