You can get a guaranteed Royal Flora, which is a flower piece of the Noblesse Oblige artifact set, by completing the "Nine Pillars of Peace" quest. You can do this quest somewhat early into the game since all you need to do is get all the Geoculus on the map and upgrade your Statue of the Seven - Geo to level 10 in order to get the quest, but there will be a strong boss fight there, but you can use multiplayer to get some help.
Completing chamber 3 of floor 6 and onwards will get you a 5 star artifact box. You can open these in your inventory to get a random 5 star artifact. Only the rewards from floor 9 and onwards will get reset about every 2 weeks or so, but floor 1~8 is only a 1 time claim.
Adventure Rank 40 Domains
You can only start getting 5 star artifacts through artifact domains when you enter the AR level 40 version of the dungeon. The rate of dropping a 5 star is about 1 out of every 3 or 4 runs, which will cost about 60 or more resin. Higher AR lvl at 45+ will have a higher chance for this.
Elite bosses (the ones that costs 40 resin) can also drop 5 star artifacts, even at around AR level 20, but it's only gladiator and wanderer's troupe set. The odds of them dropping depends on your world level, that increases every 5 AR level past 20. It's not worth spamming the fights with 40 resin to hope for a 5 star though, since the resins are better used for talent books, mora, character exp early on.
The same goes for Dvalin, and Andrius boss fights. These costs 60 resins and also has a chance to drop 5 star berserker, or wanderer's troupe artifact sets. You can only do them once a week, but they also drop weapon crafting materials, so it's recommended that you do them once a week.