I think what I would say is that it is a lot easier to run 5e roughly RAW and not run headlong into glaring and gaping problems than in previous editions. To be clear, there are still 'broken' things in the game (the whole 'rulings, not rules' design philosophy made pretty clear that the creators were not going to torture their product into becoming immune to cracking). They just aren't the kind of things you 'can't not see.'
Using CodZilla as an example, there's no opening the PhB and saying, "wow, why would a druid ever not take Natural Spell as soon as they qualify?," nor is there Divine Metamagic and Persistent spell as feat options in the same splatbook.
I think you really have to want to break 5e open to find "brokenness" (and by that I don't just mean clearly better and worse options, but some vague idea of the entire game playing quite differently before and after one discovers and implements a specific exploit).
Thinking back to 3e, and comparing it to 5e:--
•Pun Pun: this one is relatively easy not to repeat. There are no obscure splat with rules on gaining godly power.
•CoDzilla: this does not show up in 5e. The concentration mechanic disrupts the basic premise. Clerics can help in combat, but the lack of extra attack means that their abilities do not scale, meaning that they have to spend their spells on helping fight, just like any other long-rest ability contributor. More broadly, while one might say that one class is a little better than another, each does their own job better than anybody else does (so there's no equivalent to "a cleric can be a better fighter than a fighter can").
•Minionmancy: Regular summoning is useful, but not insane (I think certain low-CR creatures are too cheap, and thus "best option," but still the spell is not the clear and obvious winner. Planar ally makes clear that it doesn't let you control the allies actions, so it is very much in DM control. Planar binding is strong, but the effort to bind a powerful creature looks like an adventure in and of itself to successfully accomplish (and thus should be worth a powerful benefit).
•Ice Assassin and the like: This is semi-avoided - Simulacrum is pretty abusable, particularly in creating a wish loop (but let's be honest, the first thing one has to do in any version of the game is tell your players, "bleat all you want, if you create a method of gaining infinite wishes, it won't work"). Regardless, it is not free like an ice assassin of an ice assassin.
•Hulking Hurler: specific example was avoided. As to the general concept of a poorly thought out situation where a rule is used in a place it was never meant to go, thus causing chaos, the closest contender is using athletics (skills in combat) as grapple, creating the rogue/bard grappling champion who is better than a barbarian (or most any monsters in the MM, since most aren't even proficient in acrobatics/athletic).
•All-access spellcasters (archivists, spell-to-power erudites, Rainbow Servant-beguiler/dread necromancer/warmage): this is half-avoided/half-embraced. There is no equivalent for across the board spell selection. Feats or class features allowing plucking 1-3 spells from another class are built into system, and the system balance (hopefully) accounts for this.
•Personal demi-planes and the like: people talked on message boards in 3e like it was normal for wizards over a certain level to never adventure in person because they were always actually astrally projected from personal demiplanes (crafted to make detection and invasion nearly impossible). I guess those campaigns don't have githyanki with silver swords. Either way, it's still possible in 5e, although astral projection has a cost.
•Shapechanging: druid shapechange still upsets a lot of people. This time by giving you a truckload of hp (effectively infinite at level 20, although enough in 1 round can still get you, as well as any non-hp related death). It doesn't make you the combat monster it did in 3e, though.
•Breaking (/maximizing) WBL: The crux of 3e is something 5e went to a lot of trouble to prevent. While there are undoubtedly infinite gp abuses (I haven't checked the price of ladders vs. 10' poles, for instance), the rules make pretty clear that you aren't going to get to turn that gp into every magic item you want unless the DM says so. Assuming the DM doesn't allow some truly out there interpretations ("It doesn't say I can't polymorph this pile of dirt into a Holy Avenger long sword."), you are stuck with the magic item support the DM lets you find for sale or you legitimately earn in your adventuring.
I'm sure some will have other examples, or disagree with my thoughts on them, but that's where I stand. There are things I don't like about 5e. There's ridiculousness stuff (one-handed quarterstaves and PAM, life clerics getting more out of goodberry than druids do, bard wrestling champions). But it is very easy to play the game without feeling it is broken unless you are actively trying.