Hi there,
I don’t think there is “just one” answer to your question. I’m aware of “promotions” (they are called different things) in a number of organisations just as I’m aware of many situations where people have to apply, pass a test and sit through an interview.
In general, the requirements for a P5 / D1 are outlined in the job description. So unless you meet them, these posts are typically out of reach. But even if you fulfil the formal criteria, these posts are not often easy to get since there is a good amount of competition to raise to that level.
Lastly, I would not say that P5/D1 is “management level” per se. There are a good number of senior advisors who are at P5 level and who I would not count as management and likewise, there are a good number of P3 / P4s who I would count as management in their respective offices (especially in the field). Then there are differences between organisations to the extent that a P4 in organisation A might have significant more power/influence/autonomy in decision making that a D1 in organisation B.
Which organisation are you interested in? Maybe there is somebody here who could give you the inside knowledge?