According to a report from Digitimes (as relayed by Gematsu), the PS5 has already shipped 3.4 million units within the first four weeks on the market. Digitimes cites “industry sources” for this report, as noted by Gematsu. This is the highest number of units shipped for a PlayStation console within the first four weeks, outpacing the behemoth PS4 and PS2. Not only that, but the report also explains that Sony expects to ship between 16 – 18 million units in 2021, due to an increase in system manufacturing over the course of next year.
It's important to note the difference between “units shipped” and “units sold.” While these two terms are closely related, they are not interchangeable. “Shipped” refers to the number of units sent to retailers to be sold. In other words, these are units that could be sitting on store shelves. It doesn't refer to consoles bought by consumers. “Sold,” however, does refer to the number of units bought by consumers, so it's important to make the distinction since publications sometimes incorrectly use them interchangeably.
However, considering the PS5 has been ostensibly sold out since it launched, the number of units sold is very likely close to the number of units shipped. For all intents and purposes, these numbers would be nearly identical since systems are swooped up by consumers (or scalpers) as soon as they become available.
While these figures aren't official, they're in line with what Sony had previously stated. In October 2020, the company explained (via the Financial Times) it expects to sell 7.8 million units by end of fiscal year on March 31, 2021, leaving eight more months to reach an additional 8 – 10 million units shipped to match the 16-18 million noted above.
For context, the PS4, which is one of the bestselling systems of all time (around the neighborhood of 113.5 million units sold), reached 14.41 million units sold within its first year on the market by the end of 2014. If Sony reaches its reported goal of 16-18 million units sold by 2021, it will have outperformed the PS4 by a substantial amount.