It doesn't take five months to realize someone has a drinking problem.
And if you fell in love with him, surely you knew him well enough to know about this problem. We don't just fall in love with people we don't know, now do we?
Running to HIS parents, no offense, does seem pretty desperate...especially after 5 months. Just leave him because you're unhappy and you know it. This isn't your struggle. It's his.