5 weeks is a long time for a calf tear to heal. Your GPs' referred you already, did he/she sugest what it might be & or advise you on what excercise you can take?
I've torn my calf muscles quite a few times & I'm usualy back running after 3 weeks rest, which makes me think it's either a very bad tear, something else, or you keep trying to run on it & it's not healing properly & therfore keeps tearing!
If I were you I'd make a private appointment at a physio/sports therapist, see what they diagnose & what treatment they suggest (probably total rest & ultra sound) & take it from there.
Best of luck,
PM