How do people get enough points for Alienware Vault and Giveaways Lvl 5?

Lots of grinding the daily stuff and using artifacts as optimally as possible, I'm currently getting between 50 and 60 ARP per day, some days is closer to 80. It still takes months to reach level 5.

Patience. Daily log in, max your ARP for the day, buy and upgrade the right artifacts to increase your ARP gains. In the long run, it will pay off. If you're looking for more details, you can probably ask in the discord. It takes a lot of time and dedication to reach high levels, but not an unreasonable amount of time.

Like Axelflox and MarvashMagalli wrote, there is no quick shortcut, it's just dedicated participation over a long period of time. Something like 60 ARP a day does add up over time. As for the vault, even if one does everything the ARP earnings are not enough to claim a top-tier game from their vault every month, maybe one per 2-3 months depending on their ARP cost.

I grinded for 1 year every day to reach level 5

yes, like the others have said, daily stuff and get every fragment and artifact you can. calculate which artifacts you should upgrade and how they should be combined. i reached tier 5 in about 10 months, and i almost never did the stupid mini games or the third steam quest (because i almost never owned the games). if you're not strategic about it, then yes, it'll take you several years. i recommend the discord for more detailed advice.

Took me nine months of doing almost every available task and slowly getting and upgrading artifacts to get from ~1200ARP to level 5.

It did take me years. :(

Cheers! :D

It's patience like everyone says, but honestly it's also more about whether it's worth it or not to you. Having to afk games weekly, afk watch streams, do the discord poll, join the community event, login every day without missing any days, etc. to maximize points is not for everyone, and you're basically guaranteed $50 at least in the us once every 3/6 months to spend on dell. Now you'll likely get a bit more, but maybe you wont. It's been decreasing as far as I can tell. So even if you made $300 every 3 months from it, it's a lot to do if you don't see it as a game, when you could comparatively just work 2 or 3 x 8 hour shifts at a min wage job and basically get that amount.

Takes about a year, 1.5 years I think to get to level 5, due to the artifacts. A lot of the people started a long time before when it was easier to get arp and level, then they reset everyone and introduced a new leveling program like now but they kept their arp to spend so they had an easy time getting the first artifact for 1k points and buying fragments to level up the artifact. (I think they've started to give away artifacts for free in the shop or in community events so that might be worth it).

For me for instance, I've never been able to get anything from the game vault. They're gone instantly so I doubt they even have 100 keys of each and what's left over isn't exactly worth it, like the xbox game pass for one month which no one cares about for instance. I just keep my points to spend them on DRP, otherwise I wouldn't even do it, most level 5 giveaways are gone before I get home from work, and I'm kinda tired of seeing mmo/mobile game/off platform stuff I can't even redeem because I gotta download the game first and redeem in game. Still, it's nice of them to do this, and I can't expect it to be perfect.

But honestly relay is an absolute nightmare to navigate.

Forget the vault. With the number of bots and alt accounts, everything is pretty much gone in less than a second.
It's not worth grinding for that. And there definitely are not enough giveaways besides loot boxes and promotional cosmetics stuff or beta keys to justify grinding.
If you're in the US, you can use your point to get Dell rewards but it's not worth it in most countries.