It depends on the length of cables, but you might be able to squeeze gigabit out of Cat5. I’ve had success running 10gbit over Cat5e in my own apartment, where the max length doesn’t exceed 10-15m.
Thank you! Maybe it will work. I could be explaining wrong. Maybe it’s not because of cat 5, all I know is when I asked google fiber about a better connection they said the building’s wiring only supported 100 megaBITs.