Known Box/Packing Variants
There are two distinct versions of the 705 set, each with minor variants.
The earliest is the flat box version. You can see it too is missing the patent text (as all 1961 sets do) and has its own unique image:

And the bottom of the box:

There are two versions, a US version with the US price $4.95 printed on the sides and a Canadian version with $5.95. The USA flat box was only produced in 1961 and did not return for the 1962 season, instead replaced by the new-for-1962 tall box version. This is discussed further later in the article.
It's unclear when the Canadian market changed over, but the flat box 705 continued production until at least 1963 in Canada, this is corroborated by paperwork in a 1963 Canadian example.
We also have the first appearance of the 705 tall box in Canada in 1964. It's possible Canada switched over as early as 1963, but it's not currently evident.
The tall box had two variants with each country's price printed on the side. Featured in the article below is the US version, however, there is another variant I've since found that breaks from the pattern. This one has no price:

It's possible this copy's price was obfuscated by a retailer or collector, however from auction images it appeared to legitimately not be present. It is an American copy (via the Shwayder Bros. instruction manual), so I'm unsure why two versions would exist. It is the only example I'm aware of with this oddity, but again, it could simply be an outlier for a multitude of reasons.
One more thing: there is the possibility another Canadian variant of the 705 exists, as the top of other tall box sets in this Canadian newspaper are printed instead of having the plain top for the 10x10, meaning the 705 could've had a similar variant. Note that it isn't pictured directly and no examples are known to exist.
For both regions, even though Canada's production continued much longer, the flat box variant is considered extremely rare.
Box/Overview
As with the tall box 702 and 703 sets from 1961, the 705 has an image on two sides and then models on the back. The images and the models are inherited directly from the earlier flat box:

The set is also topped with a familiar 10x10 baseplate in red.
Unlike the 702 and 703, however, the 705 also has printing on the bottom flap. Here it is compared to the 702(far left), 605 and 905.
Contents
As with the other tall box basic sets, the 705 carried a general assortment of mostly red/white parts. It is, however, the only tall box set to include a 10x20 baseplate:
The flat box set would've carried a very similar, if not the same, assortment as the advertised piece count stays consistent from 1961-1965.
Historical Examples
This section will be used for the 705's flat box variant, as I find that much more interesting and there is not much else to discuss regarding the later box.
It appears very rarely in the USA in 1961, with two appearances in the 1961-62 pack-in brochures. Most early adverts for the USA completely omit the 705, aside from later (into 1963) prepared photographs by dealers or stores themselves.
But beyond that, there are a few images of the final box that were available in 1961 media, all of which from Canada. This one is Eaton's:

The Canadian department store Morgan's also had its own unique image in 1961:

1961 USA advertisements, however, are largely missing the 705's flat box. Check out this very common advertisement from 1961, where all 1961 sets are pictured with their final box except the 705, which is missing entirely:

That omission (along with the meta knowledge we have that the set changed design in 1962) feels very purposeful. It could be an indication that the decision to redesign the set was made in late 1961, some time before November (when USA advertisements began appearing).
If true, that means the USA flat box 705 was only in production for a few months, though it is entirely possible there was holdover production into 1962, and of course as mentioned above the Canadian variant was produced into at least 1963.