In reply to Sam W:
A quick Google says no, even though the RS505 are the older 105 levers - and the ugliest shifters in existence! The RS505 use the BH59 hose, but the R7020 uses the BH90 hose.
However, the difference is minimal and, anecdotally, it's possible and people have done it.
Your other option is to go for the RS685 shifters, which are compatible and a heck of a lot nicer looking than the RS505. I've got a set of them and the RS785 post-mount calipers in a box in the garage, pending whenever I get the time to fit them!
Post edited at 21:28