Adventure Rank Up Issue (Genshin Impact)

I stopped at level 5 when I was following the storyline, you need to go to the temple near Monstand (mb wrote it wrong, I don't remember) after fighting the dragon in the city, but there again you need an adventure rank like 10-12, and that's the whole problem ... I tried to run to look for all sorts of quests on the map, but did not understand the system and it happens when I ran along the map somewhere for this quest (not on the map of the game, but ready with all sorts of chests, etc.), then at the place of the task it was not or it was not clear how to get it ... And after these errands back and forth for about 2 hours, I got tired of the rank because the rank did not even increase by 1 after opening chests, battles with mobs, and so on. Who can help with solving the problem I will be grateful