I pull cat5e for work quite often. 350' is the rule of thumb we use. I believe the actual rating is 320' though. Practical experience however shows that you can run into problems with notably shorter, and also have no problems at all with notably longer distances.
A quick Google shows that at 9600 bps your recommended distance is 15 meters or about 50'. Distance drops with higher data rates - double the data rate, halve the distance. Better/worse performance also comes with better/worse cable. And the actual application makes a difference as to how reliable the communication needs to be. I use a kluged serial-rj11 cable to talk to Hughes Personal Earth Stations from my laptop that's at least 15' but that doesn't need to be "reliable" as such. So more than one variable to consider.