Dear UserName123~
Welcome here to the Forum, I'm very sorry for your situation but think coming here is a good move. As you said this problem does surface here at times and you may get a variety of views.
For you it is realy horrible, being lied to, his having secrets and a lack of leading in intimacy are things that are so bad to bear. For many there may be a feeling that one is not attractive enough or valued.
Can I suggest you see if you can find professional advice and support? It may give you the facts for you to decide what is possible, and also support you as you go on
I'm afraid the kindest thing to do is to be blunt, though I doubt I'll say anything you have not though of for yourself. You write as a realistic and strong person, one who simply does not have a clear easy to choose path in front of her.
To over-simplify a bit there appear to be three choices in front of you, and I'll try not to influence you thinking, just lay out the options.
The first is to do nothing and accept the situation. This of course means the effects you are feeling now may well continue, maybe get worse and maybe even give negative feelings about yourself. It would probably not be good for your husband either as he may constantly know he is letting you down. It may lead to confrontations or drifting apart in the future
The second is to separate, either on a temporary or permanent basis. You said you love him and have had 5 years together, that is a lot to give away, but may be necessary if you cannot bear to live together
The third is to live with someone who has a long standing addition -and all the dishonesty it entails- while both of you try to overcome it. This is no easy path, no addiction is. On the up-side you have know there has been a problem for a long time and have been able to confront your husband and get him to admit (when backed into a corner) that he has a problem
He has agreed professional help is necessary, and you are both talking about it, hopefully nothing still hidden. Addiction normally has a cause, and in this case it sounds as this came into effect before you were on the scene. Understanding and encouragement of his victories along with professional assistance does help, but not everyone can do this
These are only broad alternatives, you -or others- may be able ot think of other ways of approaching the matter.
May I also ask if you have anyone you can discuss this with? Though hard to bring up it can help not to deal with it alone
Croix