Yeah the game has no "take 20" rule...no retries until a long rest is how I run it.
Is the intent of the 5e skill system to basically allow retries on a failure? I am not talking about a retry if you fail to persuade someone. I am talking specifically about:
1. Lockpicking. The DCs are so low that it wouldn't take even someone not proficient in thieves' tools and with a 12 Dex more than a minute to pick most locks. Seems too easy.
2. Manacles. The strength DC is low enough that if you allow a retry almost anyone can break through them in a minute's time.
My house rule is that with lockpicking you can retry but if you fail by 5 or more you break the pick off in the lock and the DC rises by a lot (and it will take time and rolls to clear the lock).
With manacles, I revert back to the old bend bars/lift gates rules from 1e and 2e wherein you get one try, and unless circumstances change (e.g. your Str goes up), then if you fail...that's it.
So I would allow a barbarian, for example, to try once to bust the manacles with his normal Str check and then if he rages I would allow another shot with advantage.
How do you handle these two items?
I'll add that I only allow those proficient with a given tool to try the related check. And something like a chance to open a lock requires proficiency with the tool, not just a high Dex.
Think of this, if you don't know about pins and tumblers, you could be a Circe de Soliel acrobat and you would never have the faintest idea how to pick a lock. Same idea for playing an instrument, creating a herbalism potion etc.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.