OP
You are in a codependent relationship with this man in addition to being his enabler and provoker because you never forget. Being all these in a relationship never works out either as you are all too clearly seeing.
What do you get out of this relationship?. What is in this for you?. You've already wasted 5 years on him and I suppose in that time you've always believed that your kindness/love for him will get him off the drink/see the error of his ways. Well it does not happen. Only HE can decide to stop drinking and he is showing no indications whatsoever of wanting to do so. And he will not do so whilst you are still around him.
And yes you are with a toxic man who will further bleed you dry emotionally. He should not be drinking alcohol ever again if he is an alcoholic. He just finds any excuse to drink, it does not matter if it is beer or spirits to him because it's all alcohol.
He doing things like buying the shopping and walking your dog are the barest of bare minimal requirements for a relationship. Why have you allowed this for yourself?. Did you see a heavily drinking parent as a child?.
This relationship is at an end anyway because his primary relationship is with drink, not you and in fact it's never been with you either. He could well go onto lose everything and everyone around him and he could still choose to drink afterwards.
Put you and your son first now and find the strength within you to get this man out of your life for good. He will continue to drag you down with him otherwise.
No wonder your son could not stand him. He has been far more sensible here than you as his mother.
What did you learn about relationships when you were growing up?. Your boundaries in relationships are well off and have likely been off beam for some years.
What do you want to teach your son about relationships and what is he learning here?. Be on your own with your son; its far better for you than to remain with a drunkard.
Do read Codependent no more by Melodie Beattie and get some therapy for yourself. Men like this take an awful long time, years even, to recover from.