I don't think there's any one answer, it depends on you, your personality, your lifestyle, etc.
For my just-turned 5 year old, I have to remind her of all that stuff too. But I'm laid back about it and it's not nagging, it's truly "reminding." I do consider a few things urgent - she recently switched to family cloth (her choice) and I remind her each time to throw it in the pail instead of the toilet. Frankly, it's hard for adults to retrain ourselves out of the habit of dropping toilet wipes into the toilet, so I don't find it frustrating - just important

My DH does not shut drawers when he opens them, so this is a testament to keep at it. Hmm, on the other hand, I'm sure his mother reminded him as a kid too. What can ya do.
Explaining WHY to do some things has been effective to get my DD to cooperate sometimes. Like the family cloth in the toilet, she knows it could break the toilet if it was flushed. Also, with the drawers being left open, someone walking by could hurt themselves if they didn't see the drawers open (a particularly salient point in our house, since I am legally blind - though I've long since learned to steer clear of the drawers anyway, given my husband's habits, lol).
I CANNOT get her to hurry when I'm in a hurry, though. I personally believe that with DD being 5, it's my responsibility to facilitate things to avoid being in a hurry. We should get ready to leave in adequate time, for example. Since I know DD doesn't move quickly, then it's up to me to make sure we've got shoes on and so on in enough time. DD doesn't go to school, but if she did, I would be teaching her to choose her clothes and pack her lunch the night before. And we'd get up in adequate time to do the things we need to do.
If for some reason I allowed a situation to get to the point of "hurry" or if it was unavoidable, I would take over. I'd grab her lunch. I'd grab her shoes. This is not universal advice, this is just how I approach it. There's nothing I can do to make DD hurry, and it just upsets everyone, so I don't feel the need to place the burden of hurry on her when she's not really capable of it and I'm perfectly capable of it. So, that's my perspective as a mom of a kid the same age.