Some news media beyond CNN are reporting on the 5 miles, such as Express News:
Since he took office in 2017, the administration has set aside $15
billion for 738 miles of walls and fencing on the 2,000-mile border,
with the money coming from Homeland Security, the Defense Department
and the Treasury Forfeiture Fund.
The federal government has completed 260 miles of replacement and
secondary walls, but only 5 new miles of the 30-foot high steel
bollard fencing where none existed before, according to U.S. Customs
and Border Protection data obtained by the Express-News.
Althought it appears to vary quite a bit: 3 miles from the Daily Mail, 16 from the Washington Post, Axios even says 0...
On the CBP (Customs and Border Protection) website, you can see where they plan to build a brand new border or replace an existing one, they even have an image (as of August 29, 2020) giving an overview:
At first sight, there is quite a lot of plain new border wall planned. On August 10, 2020, they indicated that 275 miles had been built, so where does the 5(-ish?) miles come from?
I checked all the national media releases on the CBP's website that have been released since early 2020 to see if a detailed reporting of "replacement vs brand new barrier" was available, but to no avail.
The CBP has apparently sent a report to news media as of May 22, which has been reported upon, but I couldn't find the original. WaPo's commentary on it:
A report from Customs and Border Protection sent to reporters on
Tuesday shows that 194 miles of wall have indeed been built —
including primary walls and secondary walls that act as reinforcement
systems. More to the point of Trump’s promise, only 16 miles of the
194 miles that have been constructed were built in places where
fencing didn’t already exist. Of the 170 miles of primary wall that
have been built, three miles are in places where no barrier existed
Along with the following image:
A border wall necessarily has a primary wall, and may have a secondary wall to help support the former. As such, replacing an existing wall (whether primary or seconday) or adding a secondary wall do not count toward the claim, only new primary wall construction is counted for "where no barrier existed", hence why the number appears so low compared to how much has been built/replaced.
WaPo also mentions that building barrier on areas where there were previously none is quite a bit more difficult:
It’s also true, though, that replacing wall is much easier than
building new wall. For one thing, the government generally already
owns the land on which the replacement wall is being built, obviating
the need to purchase or seize property. For another, the areas being
replaced are also generally ready for building in a way that newly
acquired territory wouldn’t be.
To sum things up: While it it difficult to pin down an exact number for today, 3 miles have been built on brand new land as of May 22, 2020 per the CBP, and with the difficulty in establishing completely new walls over simply replacing existing ones, would indicate that the claim is likely true.