Finding the 005 Discovery Set's Release Date
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The 005 Discovery Set has been one of the hardest set releases for the LEGO Samsonite community to date, and there is wide disagreement and contradiction between catalog sources.
So when did the 005 actually release? Based on previously published information, The Unofficial LEGO Collector's Guide posits 1966. BrickLink and a few other sites say 1967-68.
This archive, however, has confirmed 1965 as the release date, and we'll cover both the investigation and the evidence below.
Compiling All Appearances
There were a lot of direct mentions of the 005 set in newspapers, a source not typically explored in LEGO research. First, let's use some of these to clear the air. The set was not an FAO Schwarz exclusive as is popularly assumed.
The set appears in a Gregg's ad from 1967:

As well as mentioned in the 1967 Marshall Fields catalog, the previously undcumented 1967 Oxydol Sampler Set, as well as other newspaper adverts from as many as twenty retailers. But the set did not release in 1967.
There are mentions of the set in newspapers as early as 1966, but they are much more uncommon and are not adverts from retailers. A 1966 letter to Santa Claus mentions the 005 set by name. I've also found a newspaper clipping from a school that ordered three of them in late 1966.
So it's interesting, right, that the 005 has an explosion of appearances in 1967 as a normal set, but not 1966. But the set evidently existed in the 1966 season, as both a school and a child were aware of it. So one must wonder exactly how the set was being distributed in 1966 such that no retailer is known to have had it. It wouldn't be an institutional only set, as a child was able to find it.
So what was the distribution of the 005 prior to 1967?
Brochures
Relatively rare and unknown are full color brochures for the 005. There exist at least four different versions of them for the 005, three of which are onsite. They are dated and covered in the article Dating Various Mail-Offer Pamphlets.
But let's put that aside and pretend we do not know the date this pamphlet was prepared. Our interest here is dating the release of the 005 itself, so let's dive into the brochure to see if there are any clues:


As the 005 only features parts from the 001 Gears and the 285 Basic Set, there's nothing much the parts themselves can tell. Most telling is that both versions of the 1x1 round brick (with and without the bottom lip) are pictured. It's hard to say when that piece was updated in North America, the typical date given is 1965.
The back page also seems as a hopeful clue, but unfortunately, dating the testimonials cannot date the release of the 005.

Now surely we're out of leads, right? Right?
What if I told you there is something else on the brochure, something that gives away the answer? What if that even though there are no surviving external textual mentions of the 005 Discovery Set in 1965, we can still reliably date the 005 set to 1965? Go ahead, scroll up. Make your best guess.
Got it? Want to continue?
The 005's Prototype Box
If you're familiar with the 005, you'll notice that its prototype box is displayed on the brochure with minor differences, i.e. the red DISCOVERY text does not appear on the final box. The fonts for the "005" and "set" were also changed at some point.
There is also the lack of the box tabs on the 005 prototype, which is something found on all of the double-stack 1965 Samsonite sets. That missing feature was also missing on the wider 1965 line's prototype boxes. When released for the 1965 season, all those sets (003, 004, 615) had tabs:

The fact that the 005 set in the brochure is missing those tabs just like the 1965 prototypes is very telling. Regardless, that is not the main piece of evidence.
Check out the profile of my copy of the 005 set:

Compare that with the prototype's side:

It's hard to make out, but the patent information is displayed differently on both. The finalized 005 box has the 1965+ format, while the prototype has... what format is that?
Well, check out the sides of 1961-1965 sets:

Do you see what I'm referring to now?
It's easier to see on the brochure's front cover, but the prototype 005's patent line is below every single LEGO logo on its box like all 1961-65 sets. Whereas on the finalized 005, the patent line is only on the front like most 1965-71 basic sets. So the prototype 005 box was printed in the 1961-65 style as opposed to the one 1965 sets used upon release.
So, let's review. The prototype 005 set lacks tabs that all 1965 double stack sets had upon release. It also has different fonts, while the finalized box is consistent with 1965 sets. And finally, the prototype's patent formatting correlates more with the 1961 sets' choice of formatting than the eventually decided 1965+ formatting.
I think that is pretty hard evidence that the set would've been released in 1965. They wouldn't have reverted back to an old format in 1966, they would've designed the 005 based on the existing sets.
But one must wonder, how was this set released in 1965. How would a set release but not be advertised?
Why is the 005 set not advertised anywhere until 1966?
Let's put aside all that we've collected and reasoned thus far, including the fact that we have a physical box that dates the promotion to 1965 (which I will show later).
Consider this: What do you think the purpose of the set was?
Look through the 005's pamphlet. Notice it is describing and demonstrating LEGO to parents who are not familiar with it. It is also offering the 005 set for 10 days free, a trial period set before they are expected to make payment(s). Even the name is important: "Discovery Set".
It also explains why the 1965 prototype 005 is featured, as the focus would be on getting the promotional materials out before the 1965 Christmas season. The largest release season in LEGO Samsonite's history with a completely redesigned line of sets. The assumption would be that these brochures would've been packed into unrelated products targeting parents starting mid-1965.
And remember, there are hints of the 005 set in 1965, as the unique owl mascot for the set appears in a plethora of 1965 ads. Just no direct mentions, which wouldn't be expected as this was a trial mail-in set offered through some unrelated product or distribution channel.
A toy store wouldn't advertise this, and again we have the 1965 brochure for the promotion:
Why would a set specifically for mail-order come in a colorful box?
There's a very common rule of thumb for LEGO Samsonite sets—anything sold via catalog sales or mail-offer came in a plain box, and colorful boxes only sold in stores.
So if you're familiar, you may ask: why the colorful box, rather than the standard plain box other mail order sets came in? It's a very reasonable question, as most mail order exclusive sets of the late 1960s and early 1970's were sold with plain boxes.
The difference, in my mind, is marketing.
A big crux of Samsonite's marketing from the beginning was "As your child's collection grows...". LEGO is not meant to be a one time buy, Samsonite wants you to go out and buy some more. That's the point of LEGO.
This set was meant to be a first impression, based on the discovery name and the brochure's characterization of the reader as unfamiliar. So when the 005 arrived, it'd have this very nice and colorful sleeve with drawers that pull out, opposed to a plain cardboard box. $9.95 was not cheap in 1965.
Also ask: if you were Samsonite, wouldn't you want parents and children to easily recognize the distinctive boxes in store?
So the 005 sits in a very peculiar spot, as it is one of the few 1965+ mail order sets that shipped with its colorful box inside a cardboard box.
And we can know this for certain, as not only has a copy from March 1966 been found with an outer shipping box, but also this early 1967 image of four 005's at a post office auction:

The 005 set is also uniquely the only 1965+ set to omit the age range printed on the side of the box. As we've shown it to be meant for mail order, that alone would explain the lack of age designation.
And here is the surviving outer mailer box for the 005, dated March 1966. That date (if you know about any other LEGO promotions) conclusively demonstrates a late 1965 availability for the 005 Discovery Set, as all Samsonite promotions began late in the year and fulfilled until ~April.

Other Considerations
Anything else?
Why does the paper trail for the 005 start in 1966? My guess would be the pamphlets were the primary way this set was marketed in 1965-66, and the 1966 mentions are just lucky appearances.
It also builds a case as to why the set didn't release to stores until 1967, as in 1965-66 it was a mail-in offer via Imaginations Inc, 1967 it was offered through Oxydol (the original brochure could've still been in circulation too), and in late 1967 onward the 005 set was offered at retail.
I know this got rather deep into the weeds and tangential, but all of what we've covered was needed in order to find the correct date.
As far as we can find, considering all the evidence laid out above, it had to have been 1965.
Wrapping Up
The release date of the 005 set is a pedantic issue, sure, but these sorts of questions lead to better informing the larger narrative. Samsonite created this set as they saw a need to convince more families of LEGO's potential.
And while we're at it, I have two more things to note. I can't help myself.
For one, there is something missing from the catalog—Samsonite! Samsonite's name appears nowhere on the 005's prototype packaging, in the pamphlet, nada. There are two possible explanations for this, neither are exclusive and the issue is not necessarily binary.
In mid-1965, Shwayder Bros. Inc. announced a rebrand to the Samsonite Corporation. That seems to also lend to a 1965 date for this prototype, as the company was in the middle of a rebrand during 1965 and there would be a level of uncertainty.
But there's another explanation that has a bit more weight to it.
Samsonite's LEGO sales were much slower compared to that of Europe's, so maybe we're seeing their attempt to push that exotic European angle on US consumers and let their own branding take a backseat? That last question plays into a larger idea I've been cooking up: compare how prominently the Samsonite name appears on 1961-65 boxes versus the shrinking of the name through 1965-71. It seemed Samsonite were adverse of their own name on LEGO products.
Onto the second note. While trying to date the testimonials, I wanted to find the period in which Benjamin Alpert was president of Childcraft. I couldn't gather enough evidence for a confident conclusion, but I did stumble upon this patent for a two-piece mold, plastic construction toy. It was submitted in 1971 by a familiar name: Benjamin Alpert
Hm... do we know any other two-piece mold plastic construction toys? It's not really the classic brick, fair, but consider their words. "At Childcraft our primary concern is to provide children with playthings that will contribute toward the development of a constructive personality...Safe, sturdy, and educationally sound, the Lego System is the kind of toy Childcraft believes will foster child development."
Within a few years of that quote, they dipped their toes in the waters of the construction toy system. It's just fascinating to see the possible impact of LEGO on the toy market, wherein companies began to consider their own angle.
I can't find any examples of this actually making it to market as there is simply no documentation or listings. It doesn't seem nearly as robust as a building system anyway, and likely wasn't intended to be used in the same way LEGO was. So don't mistake this as me calling them a copycat; they were doing their own thing.