New fibre internal house connect

Does Telus need to place another cat5e for the fibre to telus tv / internet router. Or can the fibre connect to Telus router using existing cat 5e that was put in originally for Telus tv.
Basically put fibre connect device unto wall inside garage and run from there using original cat5e to Telus router for Optik tv T3200M. Is there a speed loss
I don’t think it makes a difference. Mine’s connected using a basic Cat5e patch cable. To my knowledge there shouldn’t be any latency issues over distance.