I started work a month ago, and i was wondering if it was professional if I started sporting a 5 o'clock shadow.
Depends on your company's practices/preferences, and depends on your role in the company.
You can generally get away with more if you aren't dealing directly with customers or suppliers, or if you're officially in the Research division (where it's generally assumed half the staff is happily and productively insane, or at least are academic weirdos).
If you are working with customers, you want to aim for being someone they're comfortable with. If you're selling to executives, you want to look like an executive; if you're dealing only with techies you still want to look like someone they can trust technically. (Old not-quite-a-joke: There was a time when you could recognize an IBM repair technician by the fact that, when he took off his navy sports coat, his sleeves were already rolled up.)
As far as advice goes: Look around the office. If the look you want to sport is common among respected people with the same sort of responsibilities you have, you can probably get away with it. If you'd be the only one, probably not. If in any doubt, you can ask your manager whether this would be considered acceptable "business casual" or not; guidance regarding company culture is one of the things managers are for.
The simple answer (especially as you work for a bank) is check your hr policy for dress code, it will have something to say on it.
But I will also suggest against it for the following reason:
A couple of years ago I was interviewing for developers at the insurance company I worked for. One guy came in, good cv, good suit, George Michael shadow. My immediate impression was someone who couldn't judge a situation well (a corporate in insurance is likely to be traditional at interview), and that set the tone, and he was out of the running from first second.
I thought later about why someone wouldn't have realised and then it hit me, he worked for a digital agency, likely dress down at work. He had dressed up in every way he could given he was returning to work after the interview (it was an early morning interview). Having a shave would have been obvious to his co-workers as going to an interview (of course I could be wrong and he just didn't get it, but he seemed smart enough otherwise).
So middle of the road is always good, easier to disguise if you need to.