The DS is out of reach in my view. It'll be a while before we see another system reach those numbers, maybe the Switch 2 can do it if Nintendo makes it fully backwards compatible and does exactly the same things they're doing with the Switch now, only double down on the marketing and support. But that won't be until waaay down the road, so I digress.
I do think it has a good chance to catch the 3DS. The 3DS is pretty much finished. It's not going to grow much more than where it is now. I'm thinking somewhere around 24.5 million will be its final tally. The Switch can reach that. As I stated in an earlier comment, it may be falling behind the 3DS in Japan right now, but the 3DS peaked very early. If fact, we just passed the 3DS' peak year, it's 2nd year (2012) whereas the Switch's peak years have yet to come. So, I think starting in 2020 is when it'll noticeably start to close the gap with the 3DS and eventually, once it gets close to the end of its cycle, it will overtake the 3DS.
And I highly doubt that we will get Switch 2 in 2022 (Switch's 5th year). Especially if the Switch continues to track well ahead of the 3DS' global sales like it has. The Switch was released in March 2017 and by that point, the 3DS had been on the market for about 6 years. So anything shorter than 6 years for the Switch would be cutting its legs off from underneath and, in my opinion, a big mistake on Nintendo's part.
As far as the PS5 and its potential effect on Switch sales are concerned, I side with Kerotan in that I don't see how one could effect the other. By the time the PS5 comes out, more than likely in late 2020, Nintendo will have made the adjustment, or start doing so by that point, of marketing and selling the Switch as a handheld device that can be played like a console. Right now, they are marketing the Switch primarily as a console you can take on the go like a portable and its price point of $300 has a lot to do with that, I feel. By that point, it will be at either $250, or even $200 if we get a revision of sorts that helps bring it down to that price. From that point onwards, they'll market the Switch as a handheld capable of HD quality games you can play on your TV. All the while, they'll be drawing in more and more of their handheld/portable audience who were waiting for the Switch to get to that handheld price range for them to make the purchase. Plus, there's the Switch Pro/X/i, whichever you prefer, that will fill the niche for those who want stronger, upgraded hardware.
Meanwhile, the PS5 will be launching at probably $400; At most, $500. And at those launch prices, the vast majority of people who will by the system are the early adapters and/or diehard, loyal PlayStation fans who are eager to get the newest system while the mainstream audience will wait for a price cut to a more affordable range and for its library to build and grow over time. Sony and Nintendo will be going for totally different audiences here and one company's performance and success will have little to no effect on the other's.
The Switch has the advantages of being their first ever hybrid. So the benefits of a console but with portability. It also has the full force of Nintendo games development focused on one platform instead of two.
I don't think a switch 2 will have the same effect. It will sell well but not as well imo.