I require training. So, while i"ve not yet run/played a 5e game, I see no reason I would not continue that. So, yes to a long rest...assuming that long rest is a minimum of 1 week +.
Depending on the group and the situation of the adventure...I have been known to let parties level up in medias res, like, usually over 8-9th level, working with the story/fluff that they are so expert in their chosen class they can [handwave] "figure out/discover" how to better themselves without mentoring. But somewhere relatively secure and some amount of time will be required. Working with a mentor at higher levels let's you level up faster (if not cheaper).
So, yes to long rest...with training....at lower levels. Shorter "long rest", possibly without training, at higher levels.