Time Machine Backup to drive shared on BTHomeHub3?
For Time Machine to back up to a disk, the disk must be formatted as Mac OS Extended to allow for the hard links and other special metadata that Time Machine uses. However, the BT Home Hub doesn't let you share such a disk over the network (haven't tried the new 5, but I know the 3 doesn't let you). This means you need to set up a sparse bundle on the disk to contain the backup. This should be done automatically, but as with everything relating to the awful BTHHs, it won't happen—afaik the Home Hub uses a non-standard method for sharing network disks. Whilst you may be able to get it working by creating your own sparse bundle using Disk Utility, then mounting that and using that as your backup destination, I wouldn't trust my backups over it.