I think part of the issue is the description - the hint that this was the end of riff 2 helped me iron out what I think you are asking about.
The 5:5 and 5:7 means string:fret as asked. It does seem like the written description is a bit confusing with the direction and string:fret being combined.
For playing, I would say that Justin is simply muting strings 5 to 1 at the last fret (7) he was on. Nothing more special than that.
the transition into the third riff starts with the slide from 5: 5-7, then mute for for 2 chugs on 6:0, then 5:7 and 6:6, then three chugs on 6:0, then the F power chord and pull off. this eventually changes into 5:7, 6:6, 6:5 and two chugs then the F power chord. I see it is written 6:1 and 6:0 to simplify and that is not what I hear - I play the F power chord (6:1 and 5:3 - 13XXXX in the text) and pull it off to go back into the chug on 6:0.
This lesson really is a hassle. It’s very unclear and the fact that the tab is not included even via the app makes it worse. I understand it is a different service, and the website is free, but I’m using the app and I don’t even have the (unclear) instructions on this web page.
If you give an exercise on the app, it should be manageable to do it without paying more via the website (which you need to be aware of)
As @stitch and @TheMadman_tobyjenner said the tab for the riff is available for free in the text below the JG website Module 12 lesson. With the paid tab service you would get the tab for the rest of the song. If you are using the app for lessons, it is always good to check the website lessons for additional information such as tabs for riffs and sometimes pdfs and GuitarPro files for song studies. The text below website lessons is also very useful for lessons with multiple chords, since it includes the chord diagrams.