While often shielded, CAT5 can be of the UTP type, meaning unshielded twisted pair. The "true" RS-485 cable you link to has two twisted pairs and a shield. If I remember right, CAT5e (and above) has a shield, at least most cables I have seen have - the exact standard can vary. I guess those would do the job just nice. Just make sure you use the twisted pair like in the original RS-485 cable (your data sheet looks like [1 White/Orange Stripe] and [2 Orange/White Stripe] are a twisted pair, and [3 Blue/White Stripe] is a third, untwisted wire.)
There seems to be a small impedance mismatch (100 Ohms for CAT5, 120 Ohms for RS-485). This will cause reflections at the driver and at the receiver, but I am pretty sure your application will still work. While you may read that 120 Ohms is typical for RS-485, the termination network uses 120 Ohms between the differential pair and 2 * 680 Ohms to VCC and GND.
Thus, the value of the termination that the cable "looks into" is smaller than 120 Ohms anyway: (120||(680+680)) Ohms = 110 Ohms.
If you have the chance to test, you could go for it. I would probably not even hesitate and use STP CAT5(e). If your contract says you pay money for every minute your installation fails, you probably want to use cables with the proper specification. (The latter will still not make sure nothing ever fails, but you're probably in a better position if you can blame it on the "true" cable instead of having someone else blaming your "wrong" cable. But you see how this last paragraph has nothing to do with physics...)