Can you actually get the 5-star equipment in the banner above the Common Relic Draw through that draw?

Here's a good source from the FFRK Subreddit FAQ:

What is the chance of pulling a <5 STAR ITEM>?

For a quick answer, you have ~0.001% chance of getting a specific 5* off a Common Relic draw, and about 1% to get a "featured" 5* off a Rare Relic draw. Common Relic Draws keep all released items, so the chance for a 5* item off of Common Relic Draw is 0.001 * the number of 5* equipment that can be pulled (a total chance of 0.034% at the time of this edit). Rare Relic Draw banners currently have a 10% chance of dropping a 5* item.

Basically, common draws could pull a 5* item, but they're so freaking rare that you're better off buying a lottery ticket in most cases.

The numbers linked are somewhat out of date (as more items have been added over time), but they seem to indicate around 73% chance of pulling a 1*, a 20% chance of 2*, a 6% chance for 3*, a tenth of a percent for 4*, and a hundredth of a percent for a 5*.

I've pulled a 3-star from the Common Relic draw, but not yet a 5-star. I think those items ARE available, but without the boosted drop rate the event Relic Draws usually have, they are exceedingly rare.

The same thing happens with the Half Price x11 Draws, to the point I've stopped throwing away Mythril on them because I've not gotten a 5-star from them yet. I'll save my Mythril for an Event draw with an item I want.

I was pretty sure it's impossible to get 5-6 star pull from the daily draw until yesterday. Over 3 years and I haven't missed many days and now I finally got one. Today I pulled another one. Feels like something might have changed.