No, if it were a 15.2 (which you may be thinking) it would never have 3 digits after the one dot in the name.
Where did you get the "running 15.201 right now" from? From Catalyst Control Center system information?
From the system information of Catalyst 15.7.1
i had (july 30, 2015) i quote :
Driver Packaging Version: 15.20.1062.1003-150728a1-187447C
I guess that's what you have, and if so that would be all right then for your HD5850.