Was it 105 from 10 years ago (105SC, which was 8-speed at the time) or from 18 years ago (6-speed at the time), etc.? Was it pre-indexed-shifting 105?

If your old bike has indexed-shifting 105, then you could swap out the deraillers. All Shimano indexed rear deraillers (except pre-9-speed Dura-Ace) have the same cable pull and are thus compatible.
Front derailler is more tricky. STI shifting is indexed front, and requires special cable pull for the front derailler, that 105 has had since 2005. If your old bike has STI shifting, then you'll probably be fine.

However, I don't think it's worth swapping out your new Sora for your old 105, unless the 105 is relatively recent. The Sora will work just as well, if not better.