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I don't think standard actions or move actions specifically state it needs to be done in your turn also. Thankfully, they don't need to because one can only perform actions on their turn besides immediate actions and free action (speak) because those ones specifically state otherwise:
In general, speaking is a free action that you can perform even when it isn't your turn. Speaking more than a few sentences is generally beyond the limit of a free action.
However, unlike a swift action, an immediate action can be performed at any time—even if it's not your turn.
A 5-foot step is a miscellaneous action that is done on your turn. There are specific cases of 5-foot stepping outside your turn, such as with the Step Up feat, but it turns that miscellaneous action into an immediate action so that it works within the rules. Readied actions also had to specifically state one can 5-foot step and even then readying an action is a special initiative-altering action that essentially let's one delay and finish part of one's turn later, but attacks of opportunities have no such exception granting a 5-foot step.