In my experience, it can work. I'm an AA member and one of the steps is to make amends. I struggled about how to make amends to my wife, we have so much history and I drank for many years. It's not like I can point to one specific incident and say "sorry bout that," besides I've said I'm sorry too many times to have it mean anything to her.
So what I learned to do is a "living amend" and that's about how I live my life everyday and how I treat my wife in our relationship. I feel privileged that she didn't kick my butt to the curb, and try to show her everyday, through my behavior (not my words) how much I appreciate that. It's taken a few years but I feel like I've regained her trust and we are probably closer know than we have ever been. Part of that is due to maturity, we are both in our late 50's and as empty nesters now we have grown closer since the kids have left.
Now the bad news, it's going to take time and effort for you to do this (if it's even possible). And you need PATIENCE! You were drunk for 25 years, that's 300 months. You've been sober 5 months. Do the math. Over the past 300 plus months you've been sober less than 2% of the months and drunk in 98% of the months. It's going to take awhile to tip the scales towards sobriety so that your wife can trust and believe in you again. For me it got gradually better but it took maybe 3 - 4 years. Best wishes to you.