Ahh..yes they do need to be warm. What type of potato salad are you making submitter?

The classic southern salad with mayo, vinegar, celery etc..etc. (many recipes out there).
But the best tip I have for that application is use dijon mustard and fresh turmeric for the flavor and color (instead of yellow mustard)..and by fresh I mean a something purchased recently..and not the one that came with a spice rack years ago it makes a world of diffrence.

Also, dress them while still warm because they'll absorb the dressing better.

Test them with a fork or knife as mentioned. They should be tender but not overly soft as you want intact bits and not mashed potatoes. I prefer red potatoes.
If you've peeled or diced them put them in stainer and let the steam and moisture evaporate. You don't want lots of moisture when you dress them and lets them soak up the dressing.

Okay, I read the rest of your question. Dice your 5 lovely potatoes into 1/2" cubes more or less. Cover them with cold water in a pot, plus salt. Boil for 10-15 minutes. Enjoy your potato salad.

Depends on their size but if they're about the size of a small lemon, probably 20 to 25 minutes. Remember to cover them with 2 inches of water!

Use a waxy potato ( new reds, Yukon golds, fingerlings) and cut them into average 1/2" cubes. Put in a pot with cold water to cover by 3" and add a tablespoon of sea or kosher salt. Bring to a boil, then reduce to an active simmer. Cooking time will depend on how many potatoes you're cooking, but for 2 1/2 to 3 pounds, it should take 15 to 20 minutes after the boil for the potatoes to be easily pierced with a sharp knife.