"It is an old film, I watched it fifteen years ago."
Translation:Это старый фильм, я смотрела его пятнадцать лет назад.
«Тому назад» is also possible but quite a bit outdated and bookish (i.e., unlikely to be used by someone younger than 50-60). Also, probably, better with bigger numbers like 100 years ago :)
We accept it in some sentences but I would not recommend using it in spoken or written speech regardless of the level or formality you are aiming at.
Well, I'm 57, so I guess that explains that. It's four-to-one on Google for 15 лет назад/15 лет тому назад; a sizeable gap, but the latter is certainly not uncommon.
Actually, I did search properly, but more properly: I wrote out пятнадцать. I guess that does strengthen the generation gap argument.
Not actually a gap... you have to know both expressions anyway. It is not like «тому назад» fell out of use centuries ago. You will still see it used in literature and Soviet era films that you CAN and SHOULD understand. The people who use it will be noticeably older than you, though. That's why I do not recommend learning it that way—even our older learners are probably not THAT old.
Anyway, judging by the corpus data, at your age you still would be an order of magnitude more likely to use just назад in speech or writing if you were a native speaker.