Many years ago I went to a presentation on Disaster Recovery. One of the classic stories told was of an accounting firm that kept their backups on-site in a fire proof safe (the best they could afford). One day there was a fire. The safe was perfectly intact, and showed no signs of any damage that would have resulted in the contents being damaged.
Unfortunately the Fire Department Standard Operating Procedure was that every fire was suspicious until proven otherwise, and the site was declared a crime scene. Consequently the Business was denied access to the site for several weeks until the situation was resolved and the remaining building could be made safe.
By that stage enough of their customers had moved to another accountancy firm and they were unable to survive with the remaining customers despite being able to completely rebuild their IT infrastructure.
I'd suggest in your example you may want to consider some form of removable media (5 GB will easily fit on a dual-layer DVD) and keep the backups in a secure safe at another family members house in case of disaster. With backups that size you could make several copies and keep them at multiple locations. Alternatively, encrypt the backups and keep a copy at work.