As this has been raised I will mention this now; I can confirm that if you are banned in RS4 you will be permitted to play in RS5 open beta, even if you have been denied for a long period or permanently denied.
Note that RS5 open beta is a test server; there will be a zero tolerance approach to intentional rule breaking, and if you are banned from there you will not be unbanned and any unban requests made for RS5 open beta will be summarily denied.
If you are permanently denied or denied for a very long time you should consider this a chance at a clean slate, if you behave well and contribute positively then we may consider lifting your ban and allowing you to play in the full release of RS5.