Retries

One of the key features of 5e is something called "bounded accuracy". Effectively, what this means is that the bonuses to various rolls are much more constrained - a character who is 'good' at something will generally find he gets most of his bonus in the first few levels, and will then only see a fairly moderate increase as time goes on. This is matched, of course, with a much more bounded set of DCs.

(There are exceptions, of course, especially if a player wants to burn a lot of resource on a particular speciality. And I exaggerate somewhat, too. But the above is a reasonably good description.)

In real play, what that means is that if the whole group rolls for something (initiative, for example), it's likely that whoever rolls best on the die will end up with the best overall total. This differs from 3e, in particular, where it was not uncommon for a character who is 'good' at something to have a bonus +20 or more higher than the character who is 'poor' at that thing.

That, of course, is something of a mixed blessing. In my opinion, though, it's a net good.

But it does have two important consequences. Firstly, the DM needs to be very wary about allowing retries, and likewise the DM needs to control group rolls quite carefully. Otherwise, the likelihood is that some of the dice will come up especially well or badly, skewing the results quite harshly.

So, here's what I recommend:

Firstly, you should only roll where there's a meaningful chance of failure. If the party want to search a room and they have all the time in the world, there's no point in rolling - they should find whatever it is that is there to be found. (Of course, it's possible that there might be something so well hidden that they can't find it, no matter how they search. But even in that case, why bother rolling - they can't find it!)

Secondly, retries should only be allowed if the situation significantly changes. (In combat, of course, the situation is constantly shifting, hence the "why can you retry an attack roll?" concundrum doens't apply.) What that means is that if the Rogue fails to open a lock, he does not get to retry unless his bonus increases, he gets a better set of tools, or something else significantly shifts - that first roll represents his best possible effort. (And note that the whole situation has to change. So if the Rogue packs a set of 'normal' tools and a set of 'masterwork' tools, he can't use them in that order to get two rolls. That is, to put not too fine a point on it, cheating.)

Thirdly, as much as possible there should be consequences for failure, and those consequences should be spelled out as clearly as possible. If the party fail to break down a door, this will notify whoever is beyond the door to their presence. The party should probably know that before the first roll. (Incidentally, this is a case where I would allow a retry... sort of. I actually wouldn't bother with the second roll - after the first failure, they can automatically break down the door, if that is at all possible... they just suffer whatever the consequences of that first failure were.) Of course, in some cases it's valid to have hidden consequences for failure - in the case of a hidden trap, or similar. But that should be the exception, not the rule.

Fourthly, in situations where the whole party engage in a single task, don't have everyone roll. Instead, have whoever declared the action first roll (since it was his idea) with advantage, representing the assistance of the rest of the party. (Conversely, if it's something like sneaking around, you probably want one person to roll with disadvantage - representing the Rogue using his advanced skill, but being hampered by the need to help the others. That gives slightly odd results, since the full-plate-wearing Fighter thus benefits from the Rogue's advanced skill, but it's not too horrible.)

Of course, don't forget that the game already has some helpful mechanisms in place for this purpose. In some cases a group check may well be appropriate (everyone rolls, and if half the party succeed then everyone succeeds; otherwise everyone fails). In other cases, Passive Perception may well apply (in an ambush, roll Stealth for the enemy and compare with the PCs' PP scores - this allows some to be surprised and not others).

I should note one other thing: unlike some DM's, I'm not of the view that you should seek to minimise the roll of the dice in the game. Rolling dice is fun, and provides a degree of uncertainty that is generally beneficial to RPGs (in my opinion). But I am aware that the dice should be used carefully, lest bizarre and unwanted results crop up and start derailing things.