Why do you want to wrap your own tubes?
What kind of strength are you expecting?
I ask out of curiosity, and not to appear condescending.. Trying to get a grasp of what you're trying to achieve..
have you searched for videos on how paper tubes are made? that might also help you with ideas on how best to approach it. getting a decent mandrel might also make the endeavour unachievable..
Oh, and remember that paper (like many things!) also has a grain. it'll form / roll / tear easier in one direction than the other.
Papier mache? like you did in art class? strips of glue-soaked paper over a waxed / wax paper covered mandrel..
LOC has a 5.38" tube, mind you it is $40!
Uline (a shipping supply company) has 5" mailing tubes, but they might be a bit heavy..
https://www.uline.ca/CustomProduct/BrowseR_Listing?subgrp=3706&diameter=5
(I's us the US has a similar supplier..)
Lastly, you might want to look at 'Sono tubes', typically at the local home / hardware store.. Tubes used to hold concrete for decks, fence posts, etc..