Although "5nm" and "7nm" look like physical measurements, they aren't; all they are is marketing labels, and the only thing you can be somewhat confident of is that if a single company has one process they call "5nm" and one they call "7nm" then the "5nm" one probably has physically smaller features and greater density of components on chip.

And although "2020" and "2021" look like actual dates, they aren't; all they are is marketing labels, because saying you're going to do something in 2020 is cheap.

So what we know is that TSMC say they are going to begin volume manufacturing of "5nm" chips in "2020" (reality: at some unknown date they will be making large quantities of chips on a process to which they have found it convenient to attach the label "5nm"), and that Intel say they are going to launch "7nm" chips in "2021" (reality: at some unknown date they will be making unknown quantities of chips on a process to which they have found it convenient to attach the label "7nm").

Whether TSMC's "2020" is really earlier than Intel's "2021", and whether TSCM's "5nm" is really denser than Intel's "7nm", who knows?

(I'd guess TSMC are in fact ahead, but this isn't a field where you want to be trusting manufacturers' announcements much.)

For what it's worth, the presentation we got from our vendor was 2020 for first 5nm silicon from TSMC.