I don’t understand what you are saying.
I have used this export method for years, so I doubt it works only for backendless 5. In Backendless 3 if you go under Console, and then select Manage / Export you can select what tables to export. Once you select them and tap Export, you are supposed to receive an email with a link (that is also the message written in Backendless), but no email with the link is received (and this stopped working a few days ago).
I recall this happened some years back as well, so you need to look into the issue and fix it as otherwise there is no other way to export the data.
Here is the only screen that can be used for data export:
And here is the message (as always, but then no email is sent):
So, can you solve this as no email is received and therefore it is impossible for me to export the data since the servers were down some days ago?